Diamond, Harold G. 1940
Overview
Works:  16 works in 125 publications in 2 languages and 3,544 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA247, 512.74 
Publication Timeline
.
Most widely held works by
Harold G Diamond
The theory of algebraic numbers by
Harry Pollard(
Book
)
27 editions published between 1975 and 2014 in English and French and held by 518 WorldCat member libraries worldwide
ProblemsV. Bases; 1. Bases and Finite Extensions; 2. Properties of Finite Extensions; 3. Conjugates and Discriminants; 4. The Cyclotomic Field; Problems; VI. Algebraic Integers and Integral Bases; 1. Algebraic Integers; 2. The Integers in a Quadratic Field; 3. Integral Bases; 4. Examples of Integral Bases; Problems; VII. Arithmetic in Algebraic Number Fields; 1. Units and Primes; 2. Units in a Quadratic Field; 3. The Uniqueness of Factorization; 4. Ideals in an Algebraic Number Field; Problems; VIII. The Fundamental Theorem of Ideal Theory; 1. Basic Properties of Ideals
27 editions published between 1975 and 2014 in English and French and held by 518 WorldCat member libraries worldwide
ProblemsV. Bases; 1. Bases and Finite Extensions; 2. Properties of Finite Extensions; 3. Conjugates and Discriminants; 4. The Cyclotomic Field; Problems; VI. Algebraic Integers and Integral Bases; 1. Algebraic Integers; 2. The Integers in a Quadratic Field; 3. Integral Bases; 4. Examples of Integral Bases; Problems; VII. Arithmetic in Algebraic Number Fields; 1. Units and Primes; 2. Units in a Quadratic Field; 3. The Uniqueness of Factorization; 4. Ideals in an Algebraic Number Field; Problems; VIII. The Fundamental Theorem of Ideal Theory; 1. Basic Properties of Ideals
Analytic number theory by Symposium in Pure Mathematics of the American Mathematical Society(
Book
)
20 editions published between 1973 and 2004 in English and held by 377 WorldCat member libraries worldwide
20 editions published between 1973 and 2004 in English and held by 377 WorldCat member libraries worldwide
Analytic number theory : an introductory course by
P. T Bateman(
Book
)
22 editions published between 2004 and 2009 in English and held by 265 WorldCat member libraries worldwide
This valuable book focuses on a collection of powerful methods ofanalysis that yield deep numbertheoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed
22 editions published between 2004 and 2009 in English and held by 265 WorldCat member libraries worldwide
This valuable book focuses on a collection of powerful methods ofanalysis that yield deep numbertheoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed
A higherdimensional sieve method : with procedures for computing sieve functions by
Harold G Diamond(
Book
)
16 editions published in 2008 in English and held by 229 WorldCat member libraries worldwide
As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated. This text explains the theory of higher dimensional sieves, examples of which are provided throughout
16 editions published in 2008 in English and held by 229 WorldCat member libraries worldwide
As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated. This text explains the theory of higher dimensional sieves, examples of which are provided throughout
Analytic number theory : proceedings of a conference in honor of Heini Halberstam by
Bruce C Berndt(
Book
)
22 editions published in 1996 in English and held by 207 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
22 editions published in 1996 in English and held by 207 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
Beurling generalized numbers by
Harold G Diamond(
Book
)
4 editions published in 2016 in English and held by 130 WorldCat member libraries worldwide
4 editions published in 2016 in English and held by 130 WorldCat member libraries worldwide
Analytic Number Theory by American Mathematical Society(
Book
)
2 editions published in 1972 in Undetermined and English and held by 3 WorldCat member libraries worldwide
2 editions published in 1972 in Undetermined and English and held by 3 WorldCat member libraries worldwide
Asymptotic distribution of generalized integers and prime numbers by
Harold G Diamond(
Book
)
3 editions published in 1965 in English and held by 3 WorldCat member libraries worldwide
The paper is divided into four chapters, of which the first two are concerned with a wide class of measures and general properties of these measures. The last two chapters deal with a few measures of prime number theoretic interest, and for these measures some special results are proved. In the first chapter 'C' and 'R' classes of measures are introduced. Convolution and certain other operations are defined and their elementary properties explored. A topology is induced in 'C' by total variation semi norms, and 'C' is shown to be a complete topological group under addition. The second chapter begins with some general results about convergence and continuity of power series in measures. C sub 1 denotes the elements of 'C' with point mass at 1, and all measures in C sub 1 is shown to be invertible in a convolution sense. The main result of the chapter is the representation of C sub 1 by 'C' under the exponential mapping. This mapping is shown to be a homeomorphism and an isomorphism of topological groups. As a corollary to this theorem the existence of nth roots of measures in C sub 1 is infered. Gprimes and integers and their related measures are defined in the third chapter. Using the results of Chapter 2, the counting measure of gintegers and Lebesgue measure is shown to be given as exponentials. The prime number theorem for gprimes is the main result of the fourth chapter
3 editions published in 1965 in English and held by 3 WorldCat member libraries worldwide
The paper is divided into four chapters, of which the first two are concerned with a wide class of measures and general properties of these measures. The last two chapters deal with a few measures of prime number theoretic interest, and for these measures some special results are proved. In the first chapter 'C' and 'R' classes of measures are introduced. Convolution and certain other operations are defined and their elementary properties explored. A topology is induced in 'C' by total variation semi norms, and 'C' is shown to be a complete topological group under addition. The second chapter begins with some general results about convergence and continuity of power series in measures. C sub 1 denotes the elements of 'C' with point mass at 1, and all measures in C sub 1 is shown to be invertible in a convolution sense. The main result of the chapter is the representation of C sub 1 by 'C' under the exponential mapping. This mapping is shown to be a homeomorphism and an isomorphism of topological groups. As a corollary to this theorem the existence of nth roots of measures in C sub 1 is infered. Gprimes and integers and their related measures are defined in the third chapter. Using the results of Chapter 2, the counting measure of gintegers and Lebesgue measure is shown to be given as exponentials. The prime number theorem for gprimes is the main result of the fourth chapter
Analytic Number Theory III : Proceedings of a Conference in Honor of Heini Halberstam(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Analytic number theory(
)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
Onesided Tauberian theorems for kernels which change sign by
Harold G Diamond(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
A new upper bound in the linear sieve and its applications by Shituo Lou(
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
In Chapter I we shall prove a new upper bound in the linear sieve. Our purpose in Chapter II is to explain our method in greater detail than was done in Chapter I. Let x be a large number. We consider $pisb2$(x)the number of prime twins not exceeding x. Using the new upper bound in the linear sieve from Chapter I, we shall prove that$$rmpisb2({x}) 0$ and x $geq$ x$sb0(epsilon), $ where$$rm H = 2{prodlimitssb{p>2}}left(1{1over(p1)sp2}right).$$In the Appendix, various computations cited in the text are given in detail
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
In Chapter I we shall prove a new upper bound in the linear sieve. Our purpose in Chapter II is to explain our method in greater detail than was done in Chapter I. Let x be a large number. We consider $pisb2$(x)the number of prime twins not exceeding x. Using the new upper bound in the linear sieve from Chapter I, we shall prove that$$rmpisb2({x}) 0$ and x $geq$ x$sb0(epsilon), $ where$$rm H = 2{prodlimitssb{p>2}}left(1{1over(p1)sp2}right).$$In the Appendix, various computations cited in the text are given in detail
Analytic number theory : proceedings of a conference in honor of Paul T. Bateman by
Bruce C Berndt(
Book
)
2 editions published in 1990 in English and held by 1 WorldCat member library 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
2 editions published in 1990 in English and held by 1 WorldCat member library 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
A sieve auxillary function by David Michael Bradley(
)
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
A sieve is a device for estimating the size of a finite set of integers after certain residue classes have been eliminated. In the sieve theories of RosserIwaniec and DiamondHalberstamRichert, the upper and lower bound sieve functions (F and f, respectively) satisfy a coupled system of differentialdifference equations with retarded arguments. To aid in the study of these functions, Iwaniec introduced a conjugate differencedifferential equation with an advanced argument, and gave a solution, q, which is analytic in the right halfplane. The analysis of the bounding sieve functions, F and f, is facilitated by an adjoint integral innerproduct relation which links the local behaviour of Ff with that of the sieve auxiliary function, q. In addition, q plays a fundamental role in determining the sieving limit of the combinatorial sieve, and hence in determining the boundary conditions of the sieve functions, F and f. The sieve auxiliary function, q, has been tabulated previously, but these data were not supported by numerical analysis, due to the prohibitive presence of highorder partial derivatives arising from the Gauss quadrature method used. In this thesis, we develop additional representations of q. Certain of these representations lead to computational methods which are amenable to detailed error analysis. We provide this error analysis, and as a consequence, we indicate how qvalues guaranteed to at least seven decimal places can be tabulated
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
A sieve is a device for estimating the size of a finite set of integers after certain residue classes have been eliminated. In the sieve theories of RosserIwaniec and DiamondHalberstamRichert, the upper and lower bound sieve functions (F and f, respectively) satisfy a coupled system of differentialdifference equations with retarded arguments. To aid in the study of these functions, Iwaniec introduced a conjugate differencedifferential equation with an advanced argument, and gave a solution, q, which is analytic in the right halfplane. The analysis of the bounding sieve functions, F and f, is facilitated by an adjoint integral innerproduct relation which links the local behaviour of Ff with that of the sieve auxiliary function, q. In addition, q plays a fundamental role in determining the sieving limit of the combinatorial sieve, and hence in determining the boundary conditions of the sieve functions, F and f. The sieve auxiliary function, q, has been tabulated previously, but these data were not supported by numerical analysis, due to the prohibitive presence of highorder partial derivatives arising from the Gauss quadrature method used. In this thesis, we develop additional representations of q. Certain of these representations lead to computational methods which are amenable to detailed error analysis. We provide this error analysis, and as a consequence, we indicate how qvalues guaranteed to at least seven decimal places can be tabulated
Analytic number theory : symposium on analytic number theory, March 2730, 1972, St. Louis, Missouri by Symposium in Pure Mathematics(
)
1 edition published in 1973 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1973 in English and held by 0 WorldCat member libraries worldwide
Analytic Number Theory : an Introductory Course by
P. T Bateman(
)
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
This valuable book focuses on a collection of powerful methods ofanalysis that yield deep numbertheoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
This valuable book focuses on a collection of powerful methods ofanalysis that yield deep numbertheoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed
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Related Identities
 Bateman, P. T. Author
 Pollard, Harry 19191985 Author
 Halberstam, H. (Heini) Other Honoree Editor
 American Mathematical Society Publisher Editor
 Galway, William F.
 Berndt, Bruce C. 1939 Other Author Editor
 Hildebrand, Adolf J. 1956 Other Editor
 Zhang, WenBin 1940
 Symposium in Pure Mathematics (1972, Saint Louis, Mo.)
 Richert, HansEgon Honoree