Berndt, Bruce C. 1939
Overview
Works:  122 works in 437 publications in 2 languages and 7,947 library holdings 

Genres:  Conference papers and proceedings Records and correspondence Biography 
Roles:  Author, Editor, Contributor, Other, Thesis advisor 
Classifications:  QA241, 510 
Publication Timeline
.
Most widely held works by
Bruce C Berndt
Ramanujan's notebooks by
Srinivasa Ramanujan Aiyangar(
Book
)
33 editions published between 1985 and 1999 in English and held by 576 WorldCat member libraries worldwide
This book constitutes the fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, perhaps the average depth in this volume is greater than in the first four. There are several results on continued fractions a subject that Ramanujan loved very much. It is the author's wish that this volume and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujan's remarkable ideas
33 editions published between 1985 and 1999 in English and held by 576 WorldCat member libraries worldwide
This book constitutes the fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, perhaps the average depth in this volume is greater than in the first four. There are several results on continued fractions a subject that Ramanujan loved very much. It is the author's wish that this volume and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujan's remarkable ideas
Ramanujan : letters and commentary by
Srinivasa Ramanujan Aiyangar(
Book
)
13 editions published in 1995 in English and held by 561 WorldCat member libraries worldwide
13 editions published in 1995 in English and held by 561 WorldCat member libraries worldwide
Number theory in the spirit of Ramanujan by
Bruce C Berndt(
Book
)
8 editions published in 2006 in English and held by 395 WorldCat member libraries worldwide
"The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Bruce Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory."Jacket
8 editions published in 2006 in English and held by 395 WorldCat member libraries worldwide
"The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Bruce Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory."Jacket
Ramanujan's lost notebook by
George E Andrews(
Book
)
34 editions published between 2005 and 2012 in English and held by 284 WorldCat member libraries worldwide
This volume is the second of approximately four volumes that the authors plan to write on Ramanujan's lost notebook, which is broadly interpreted to include all material published in The Lost Notebook and Other Unpublished Papers in 1988. The primary topics addressed in the authors' second volume on the lost notebook are qseries, Eisenstein series, and theta functions. Most of the entries on qseries are located in the heart of the original lost notebook, while the entries on Eisenstein series are either scattered in the lost notebook or are found in letters that Ramanujan wrote to G.H. Hardy from nursing homes. About Ramanujan's Lost Notebook, Volume I: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."  Gazette of the Australian Mathematical Society "...the results are organized topically with crossreferences to the identities as they appear in the original Ramanujan manuscript. Particularly helpful are the extensive references, indicating where in the literature these results have been proven or independently discovered as well as where and how they have been used."  Bulletin of the American Mathematical Society "The mathematics community owes a huge debt of gratitude to Andrews and Berndt for undertaking the monumental task of producing a coherent presentation along with complete proofs of the chaotically written mathematical thoughts of Ramanujan during the last year of his life. Some 85 years after his death, beautiful "new" and useful results of Ramanujan continue to be brought to light."  Mathematical Reviews
34 editions published between 2005 and 2012 in English and held by 284 WorldCat member libraries worldwide
This volume is the second of approximately four volumes that the authors plan to write on Ramanujan's lost notebook, which is broadly interpreted to include all material published in The Lost Notebook and Other Unpublished Papers in 1988. The primary topics addressed in the authors' second volume on the lost notebook are qseries, Eisenstein series, and theta functions. Most of the entries on qseries are located in the heart of the original lost notebook, while the entries on Eisenstein series are either scattered in the lost notebook or are found in letters that Ramanujan wrote to G.H. Hardy from nursing homes. About Ramanujan's Lost Notebook, Volume I: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."  Gazette of the Australian Mathematical Society "...the results are organized topically with crossreferences to the identities as they appear in the original Ramanujan manuscript. Particularly helpful are the extensive references, indicating where in the literature these results have been proven or independently discovered as well as where and how they have been used."  Bulletin of the American Mathematical Society "The mathematics community owes a huge debt of gratitude to Andrews and Berndt for undertaking the monumental task of producing a coherent presentation along with complete proofs of the chaotically written mathematical thoughts of Ramanujan during the last year of his life. Some 85 years after his death, beautiful "new" and useful results of Ramanujan continue to be brought to light."  Mathematical Reviews
Ramanujan : essays and surveys by
Srinivasa Ramanujan Aiyangar(
Book
)
10 editions published between 2001 and 2002 in English and held by 279 WorldCat member libraries worldwide
10 editions published between 2001 and 2002 in English and held by 279 WorldCat member libraries worldwide
Analytic number theory : proceedings of a conference in honor of Paul T. Bateman by
Bruce C Berndt(
Book
)
13 editions published in 1990 in English and held by 278 WorldCat member libraries worldwide
On April 2527, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa℗Ư sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe℗Ư matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fiftyfour talks, including ten in℗Ư vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H.L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R.C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory
13 editions published in 1990 in English and held by 278 WorldCat member libraries worldwide
On April 2527, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa℗Ư sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe℗Ư matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fiftyfour talks, including ten in℗Ư vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H.L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R.C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory
Chapter 9 of Ramanujan's second notebook : infinite series identities, transformations, and evaluations by
Bruce C Berndt(
Book
)
15 editions published in 1983 in English and held by 277 WorldCat member libraries worldwide
15 editions published in 1983 in English and held by 277 WorldCat member libraries worldwide
Gauss and Jacobi sums by
Bruce C Berndt(
Book
)
10 editions published between 1997 and 1998 in English and Spanish and held by 254 WorldCat member libraries worldwide
10 editions published between 1997 and 1998 in English and Spanish and held by 254 WorldCat member libraries worldwide
Analytic number theory by
Bruce C Berndt(
Book
)
28 editions published in 1996 in English and held by 242 WorldCat member libraries worldwide
On May 16 20, 1995, approximately 150 mathematicians gathered at the Conference Center of the University of Illinois at Allerton Park for an Inter national Conference on Analytic Number Theory. The meeting marked the approaching official retirement of Heini Halberstam from the mathematics fac ulty of the University of Illinois at UrbanaChampaign. Professor Halberstam has been at the University since 1980, for 8 years as head of the Department of Mathematics, and has been a leading researcher and teacher in number theory for over forty years. The program included invited one hour lectures by G. Andrews, J. Bour gain, J.M. Deshouillers, H. Halberstam, D.R. HeathBrown, H. Iwaniec, H.L. Montgomery, R. Murty, C. Pomerance, and R.C. Vaughan, and almost one hundred other talks of varying lengths. These volumes comprise contributions from most of the principal speakers and from many of the other participants, as well as some papers from mathematicians who were unable to attend. The contents span a broad range of themes from contemporary number theory, with the majority having an analytic flavor
28 editions published in 1996 in English and held by 242 WorldCat member libraries worldwide
On May 16 20, 1995, approximately 150 mathematicians gathered at the Conference Center of the University of Illinois at Allerton Park for an Inter national Conference on Analytic Number Theory. The meeting marked the approaching official retirement of Heini Halberstam from the mathematics fac ulty of the University of Illinois at UrbanaChampaign. Professor Halberstam has been at the University since 1980, for 8 years as head of the Department of Mathematics, and has been a leading researcher and teacher in number theory for over forty years. The program included invited one hour lectures by G. Andrews, J. Bour gain, J.M. Deshouillers, H. Halberstam, D.R. HeathBrown, H. Iwaniec, H.L. Montgomery, R. Murty, C. Pomerance, and R.C. Vaughan, and almost one hundred other talks of varying lengths. These volumes comprise contributions from most of the principal speakers and from many of the other participants, as well as some papers from mathematicians who were unable to attend. The contents span a broad range of themes from contemporary number theory, with the majority having an analytic flavor
Ramanujan's forty identities for the RogersRamanujan functions by
Bruce C Berndt(
Book
)
10 editions published in 2007 in English and held by 241 WorldCat member libraries worldwide
10 editions published in 2007 in English and held by 241 WorldCat member libraries worldwide
Continued fractions : from analytic number theory to constructive approximation : a volume in honor of L.J. Lange : continued
fractions, from analytic number theory to constructive approximation, May 2023, 1998, University of MissouriColumbia by
L. J Lange(
Book
)
13 editions published in 1999 in English and held by 223 WorldCat member libraries worldwide
13 editions published in 1999 in English and held by 223 WorldCat member libraries worldwide
Qseries with applications to combinatorics, number theory, and physics : a conference on qseries with applications to combinatorics,
number theory, and physics, October 2628, 2000, University of Illinois by number theory, and physics Conference on qseries with applications to combinatorics(
Book
)
10 editions published in 2001 in English and held by 218 WorldCat member libraries worldwide
10 editions published in 2001 in English and held by 218 WorldCat member libraries worldwide
Hecke's theory of modular forms and Dirichlet series by
Bruce C Berndt(
Book
)
17 editions published between 2008 and 2011 in English and Undetermined and held by 175 WorldCat member libraries worldwide
This book is an amplified and uptodate version of the first named author's lectures at the University of Illinois at UrbanaChampaign, based on Hecke's notes. Providing many details omitted from Hecke's notes, it includes various new and important developments in recent years. In particular, several generalizations and analogues of the original Hecke theory are briefly described in this concise volume
17 editions published between 2008 and 2011 in English and Undetermined and held by 175 WorldCat member libraries worldwide
This book is an amplified and uptodate version of the first named author's lectures at the University of Illinois at UrbanaChampaign, based on Hecke's notes. Providing many details omitted from Hecke's notes, it includes various new and important developments in recent years. In particular, several generalizations and analogues of the original Hecke theory are briefly described in this concise volume
Ramanujan's notebooks by
Srinivasa Ramanujan Aiyangar(
Book
)
15 editions published between 1985 and 2012 in English and Undetermined and held by 70 WorldCat member libraries worldwide
During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature
15 editions published between 1985 and 2012 in English and Undetermined and held by 70 WorldCat member libraries worldwide
During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature
Number theory and modular forms : papers in memory of Robert A. Rankin by
Robert A Rankin(
Book
)
8 editions published between 2003 and 2011 in English and held by 58 WorldCat member libraries worldwide
Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms
8 editions published between 2003 and 2011 in English and held by 58 WorldCat member libraries worldwide
Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms
Ramanujan's notebooks by
Srinivasa Ramanujan Aiyangar(
Book
)
14 editions published between 1989 and 1999 in English and held by 55 WorldCat member libraries worldwide
During the years 19031914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the second of four volumes devoted to the editing of Ramanujan's Notebooks. Part I, published in 1985, contains an account of Chapters 19 in the second notebook as well as a description of Ramanujan's quarterly reports. In this volume, we examine Chapters 1015 in Ramanujan's second notebook. If a result is known, we provide references in the literature where proofs may be found; if a result is not known, we attempt to prove it. Not only are the results fascinating, but, for the most part, Ramanujan's methods remain a mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujan's thoughts and further develop his beautiful ideas
14 editions published between 1989 and 1999 in English and held by 55 WorldCat member libraries worldwide
During the years 19031914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the second of four volumes devoted to the editing of Ramanujan's Notebooks. Part I, published in 1985, contains an account of Chapters 19 in the second notebook as well as a description of Ramanujan's quarterly reports. In this volume, we examine Chapters 1015 in Ramanujan's second notebook. If a result is known, we provide references in the literature where proofs may be found; if a result is not known, we attempt to prove it. Not only are the results fascinating, but, for the most part, Ramanujan's methods remain a mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujan's thoughts and further develop his beautiful ideas
Ramanujan's lost notebook by
Srinivasa Ramanujan Aiyangar(
Book
)
11 editions published between 2008 and 2009 in English and held by 27 WorldCat member libraries worldwide
This is the second volume devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook
11 editions published between 2008 and 2009 in English and held by 27 WorldCat member libraries worldwide
This is the second volume devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook
Ramanujan's lost notebook by
George E Andrews(
Book
)
10 editions published in 2013 in English and held by 10 WorldCat member libraries worldwide
????In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, 'Ramanujan's lost notebook.' Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.This volume is the fourth of five volumes that the authors plan to write on Ramanujan's lost notebook.? In contrast to the first three books on Ramanuj
10 editions published in 2013 in English and held by 10 WorldCat member libraries worldwide
????In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, 'Ramanujan's lost notebook.' Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.This volume is the fourth of five volumes that the authors plan to write on Ramanujan's lost notebook.? In contrast to the first three books on Ramanuj
Ramanujan's lost notebook by
George E Andrews(
Book
)
11 editions published between 2012 and 2013 in English and held by 10 WorldCat member libraries worldwide
Annotation
11 editions published between 2012 and 2013 in English and held by 10 WorldCat member libraries worldwide
Annotation
Ramanujan's lost notebook by
George E Andrews(
Book
)
3 editions published in 2005 in English and held by 1 WorldCat member library worldwide
This is the first of approximately four volumes devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook
3 editions published in 2005 in English and held by 1 WorldCat member library worldwide
This is the first of approximately four volumes devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook
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Related Identities
 Ramanujan Aiyangar, Srinivasa 18871920 Honoree Author Dedicatee
 Andrews, George E. 1938 Author Editor
 Knopp, Marvin Isadore 1933
 Hecke, Erich 18871947
 Rankin, Robert A. (Robert Alexander) 1915 Honoree Author Editor
 Ono, Ken 1968 Editor
 Joshi, Padmini T. 1927 Editor
 Bateman, P. T. Honoree Dedicatee
 Lange, L. J. (Leo Jerome) 1928 Other Honoree Author Dedicatee
 Williams, Kenneth S.
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Associated Subjects
Awards Canada College teachers Combinatorial identities Continued fractions Dirichlet series Eisenstein series Field theory (Physics) Forms, Modular Forms (Mathematics) Fourier analysis Functions Functions, Special Functions, Theta Functions of complex variables Gaussian sums Generating functions Geometry, Algebraic Global analysis (Mathematics) Hecke operators India Jacobi sums Lecturers Mathematical analysis Mathematicians Mathematics Modular functions Number theory Partitions (Mathematics) Power series qseries Ramanujan Aiyangar, Srinivasa, Research Scientists Sequences (Mathematics) Series, Infinite Transformations (Mathematics) United States Universities and collegesFaculty
Alternative Names
Berndt, B. 1939
Berndt, Bruce
Berndt, Bruce 1939
Berndt, Bruce C.
Berndt, Bruce Carl 1939
Bruce Berndt mathématicien américain
Bruce Berndt USamerikanischer Mathematiker
Bruce C. Berndt Amerikaans wiskundige
Bruce C. Berndt amerikansk matematikar
Bruce C. Berndt amerikansk matematiker
Bruce C. Berndt biografía, matemático estadounidense
バーント, B. C
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