Harold G. Diamond's Books

Harold G. Diamond and Wen-Bin Zhang (Cheung Man Ping)

By: Harold G. Diamond,Wen-Bin Zhang (Cheung Man Ping

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Harold G. Diamond and Wen-Bin Zhang (Cheung Man Ping)

By: Harold G. Diamond,Wen-Bin Zhang (Cheung Man Ping

Generalized numbers” is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L2 PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions “equivalent” to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the smooth number formulas of Dickman and de Bruijn.

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Page Count

258

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470430452

ISBN 13

9781470430450

The Theory of Algebraic Numbers

By: Harry Pollard,Harold G. Diamond

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The Theory of Algebraic Numbers

By: Harry Pollard,Harold G. Diamond

Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition.

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Page Count

196

Publisher

Courier Corporation

Published Date

ISBN 10

0486154378

ISBN 13

9780486154374

Analytic Number Theory

An Introductory Course

By: P. T. Bateman,Harold G. Diamond

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Analytic Number Theory

An Introductory Course

By: P. T. Bateman,Harold G. Diamond

This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (?elementary?) and complex variable (?analytic?) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at http: //www.math.uiuc.edu/ diamond/

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378

Publisher

World Scientific

Published Date

ISBN 10

9812560807

ISBN 13

9789812560803

A Higher-Dimensional Sieve Method

With Procedures for Computing Sieve Functions

By: Harold G. Diamond,H. Halberstam,William F. Galway

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A Higher-Dimensional Sieve Method

With Procedures for Computing Sieve Functions

By: Harold G. Diamond,H. Halberstam,William F. Galway

Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathematica® which aid in the computation of such functions.

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Page Count

266

Publisher

Cambridge University Press

Published Date

ISBN 10

113947491X

ISBN 13

9781139474917

The Theory of Algebraic Numbers: Second Edition

By: Harry Pollard,Harold G. Diamond

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The Theory of Algebraic Numbers: Second Edition

By: Harry Pollard,Harold G. Diamond

This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.

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Page Count

175

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1614440093

ISBN 13

9781614440093

A Higher-Dimensional Sieve Method

With Procedures for Computing Sieve Functions

By: Harold G. Diamond,H. Halberstam,William F. Galway

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A Higher-Dimensional Sieve Method

With Procedures for Computing Sieve Functions

By: Harold G. Diamond,H. Halberstam,William F. Galway

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Page Count

266

Publisher

Cambridge University Press

Published Date

ISBN 10

113947491X

ISBN 13

9781139474917

Book's by Harold G. Diamond

Harold G. Diamond and Wen-Bin Zhang (Cheung Man Ping)

Harold G. Diamond and Wen-Bin Zhang (Cheung Man Ping)

The Theory of Algebraic Numbers

The Theory of Algebraic Numbers

Analytic Number Theory

Analytic Number Theory

A Higher-Dimensional Sieve Method

A Higher-Dimensional Sieve Method

The Theory of Algebraic Numbers: Second Edition

The Theory of Algebraic Numbers: Second Edition

A Higher-Dimensional Sieve Method

A Higher-Dimensional Sieve Method

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