Jorgenson, Jay
Overview
Works:  36 works in 173 publications in 3 languages and 3,318 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Other, Creator 
Classifications:  QA3, 515.353 
Publication Timeline
.
Most widely held works by
Jay Jorgenson
Basic analysis of regularized series and products by
Jay Jorgenson(
Book
)
17 editions published in 1993 in English and held by 323 WorldCat member libraries worldwide
Analytic number theory and part of the spectral theory of operators (differential, pseudodifferential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of noncompact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and Lfunctions of number theory or representation theory and modular forms; to Selberglike zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is selfcontained (except for farreaching examples), requiring only standard knowledge of analysis
17 editions published in 1993 in English and held by 323 WorldCat member libraries worldwide
Analytic number theory and part of the spectral theory of operators (differential, pseudodifferential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of noncompact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and Lfunctions of number theory or representation theory and modular forms; to Selberglike zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is selfcontained (except for farreaching examples), requiring only standard knowledge of analysis
Explicit formulas for regularized products and series by
Jay Jorgenson(
Book
)
18 editions published in 1994 in English and German and held by 319 WorldCat member libraries worldwide
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3manifolds are given as a significant example
18 editions published in 1994 in English and German and held by 319 WorldCat member libraries worldwide
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3manifolds are given as a significant example
Posn̳(R) and Eisenstein series by
Jay Jorgenson(
Book
)
25 editions published in 2005 in English and held by 283 WorldCat member libraries worldwide
Annotation
25 editions published in 2005 in English and held by 283 WorldCat member libraries worldwide
Annotation
Spherical inversion on SLn̳(R) by
Jay Jorgenson(
Book
)
9 editions published in 2001 in English and held by 249 WorldCat member libraries worldwide
The essential features of HarishChandra theory are exhibited on SL[subscript n](R), but hundreds pages of background can be replaced by short direct verifications. The material becomes accessible to graduate students with essentially no background in Lie groups and representation theory. Spherical inversion is sufficient to deal with the heat kernel, which is at the center of the authors' current research. The book will serve as a selfcontained background for parts of this research."Jacket
9 editions published in 2001 in English and held by 249 WorldCat member libraries worldwide
The essential features of HarishChandra theory are exhibited on SL[subscript n](R), but hundreds pages of background can be replaced by short direct verifications. The material becomes accessible to graduate students with essentially no background in Lie groups and representation theory. Spherical inversion is sufficient to deal with the heat kernel, which is at the center of the authors' current research. The book will serve as a selfcontained background for parts of this research."Jacket
Spectral asymptotics on degenerating hyperbolic 3manifolds by
Józef Dodziuk(
Book
)
15 editions published between 1988 and 1998 in English and Italian and held by 241 WorldCat member libraries worldwide
Content Description
15 editions published between 1988 and 1998 in English and Italian and held by 241 WorldCat member libraries worldwide
Content Description
Heat Eisenstein series on SL[subscript n](C) by
Jay Jorgenson(
Book
)
14 editions published in 2009 in English and held by 211 WorldCat member libraries worldwide
14 editions published in 2009 in English and held by 211 WorldCat member libraries worldwide
The ubiquitous heat kernel : AMS special session, the ubiquitous heat kernel, October 24, 2003, Boulder, Colorado by AMS Special session on the ubiquitous heat kernel(
Book
)
12 editions published in 2006 in English and held by 205 WorldCat member libraries worldwide
12 editions published in 2006 in English and held by 205 WorldCat member libraries worldwide
Collected papers by
Serge Lang(
Book
)
9 editions published between 2000 and 2013 in English and held by 158 WorldCat member libraries worldwide
9 editions published between 2000 and 2013 in English and held by 158 WorldCat member libraries worldwide
The heat kernel and theta inversion on SL₂(C) by
Jay Jorgenson(
Book
)
16 editions published between 2008 and 2010 in English and held by 112 WorldCat member libraries worldwide
"The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL[subscript 2](C). The authors begin with the realization of the heat kernel on SL[subscript 2](C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side. By focusing on the case of SL[subscript 2](Z[i]) acting on SL[subscript 2](C), the authors are able to emphasize the importance of specific examples of the general theory of the general Selberg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zeta functions, where each conjectured step would include lower level zeta functions as factors in functional equations."Jacket
16 editions published between 2008 and 2010 in English and held by 112 WorldCat member libraries worldwide
"The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL[subscript 2](C). The authors begin with the realization of the heat kernel on SL[subscript 2](C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side. By focusing on the case of SL[subscript 2](Z[i]) acting on SL[subscript 2](C), the authors are able to emphasize the importance of specific examples of the general theory of the general Selberg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zeta functions, where each conjectured step would include lower level zeta functions as factors in functional equations."Jacket
Bounds for Green's functions on hyperbolic Riemann surfaces of finite volume by
Naga Venkata Anilatmaja Aryasomayajula(
)
1 edition published in 2013 in German and held by 16 WorldCat member libraries worldwide
1 edition published in 2013 in German and held by 16 WorldCat member libraries worldwide
Number theory, analysis and geometry : in memory of Serge Lang by
D Goldfeld(
Book
)
5 editions published in 2012 in English and held by 10 WorldCat member libraries worldwide
5 editions published in 2012 in English and held by 10 WorldCat member libraries worldwide
Collected papers by
Serge Lang(
Book
)
3 editions published between 2000 and 2001 in English and held by 9 WorldCat member libraries worldwide
3 editions published between 2000 and 2001 in English and held by 9 WorldCat member libraries worldwide
Collected papers by
Serge Lang(
Book
)
1 edition published in 2000 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2000 in English and held by 8 WorldCat member libraries worldwide
Travels through France and Germany in the years 1815, 1816, & 1817 : comprising a view of the moral, political, and social
state of those countries : interspersed with numerous historical and political anecdotes derived from authentic sources by
Jørgen Jürgensen(
Book
)
2 editions published in 1817 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1817 in English and held by 5 WorldCat member libraries worldwide
Travels through France and Germany, in the years 1815, 1816, and 1817 by
Jay Jorgenson(
Book
)
1 edition published in 1817 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1817 in English and held by 4 WorldCat member libraries worldwide
Faltings' delta function and analytic torsion for line bundles by
Jay Jorgenson(
)
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
Number Theory, Analysis and Geometry In Memory of Serge Lang by
D Goldfeld(
)
1 edition published in 2012 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 3 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Lang, Serge 19272005 Honoree Author Editor Creator
 Goldfeld, D. (Dorian) Author Editor Creator
 Dodziuk, Józef 1947 Author
 Walling, Lynne 1958 Editor
 SpringerLink (Service en ligne)
 Jones, Peter Editor
 Ribet, Kenneth A.
 Ramakrishnan, Dinakar
 Tate, John
 Aryasomayajula, Naga Venkata Anilatmaja Author
Associated Subjects
Algebra Asymptotic expansions Decomposition (Mathematics) Differential equations, Partial Eisenstein series France Functions, Theta Functions, Zeta Function spaces Geometry Geometry, Algebraic Geometry, Hyperbolic Germany Global analysis (Mathematics) Global differential geometry Group theory Harmonic analysis Heat equation Hyperbolic spaces Jacobi forms Kernel functions Lang, Serge, Lie groups Mathematical analysis Mathematics Number theory Operator theory Photography, Erotic Photography of men Sequences (Mathematics) Spectral theory (Mathematics) Spherical functions Topological groups Travel