Analytic Number Theory

An Introductory Course(Reprinted 2009)

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Number Theory
Cover of the book Analytic Number Theory by Paul T Bateman, Harold G Diamond, World Scientific Publishing Company
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Author: Paul T Bateman, Harold G Diamond ISBN: 9789814365567
Publisher: World Scientific Publishing Company Publication: September 7, 2004
Imprint: WSPC Language: English
Author: Paul T Bateman, Harold G Diamond
ISBN: 9789814365567
Publisher: World Scientific Publishing Company
Publication: September 7, 2004
Imprint: WSPC
Language: English

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/.

Contents:

  • Calculus of Arithmetic Functions
  • Summatory Functions
  • The Distribution of Prime Numbers
  • An Elementary Proof of the PNT
  • Dirichlet Series and Mellin Transforms
  • Inversion Formulas
  • The Riemann Zeta Function
  • Primes in Arithmetic Progressions
  • Applications of Characters
  • Oscillation Theorems
  • Sieves
  • Application of Sieves
  • Appendix: Results from Analysis and Algebra

Readership: Graduate students, academics and researchers interested in analytic number theory.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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/.

Contents:

Readership: Graduate students, academics and researchers interested in analytic number theory.

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