Riemann Zeta-function : The Theory of the Riemann Zeta-function with Applications (Pure & Applied Mathematics S.)

Riemann Zeta-function : The Theory of the Riemann Zeta-function with Applications (Pure & Applied Mathematics S.)

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  • 製本 Hardcover:ハードカバー版／ページ数 536 p.
  • 言語 ENG
  • 商品コード 9780471806349
  • DDC分類 515.982

Full Description

This book provides both classical and new results in Reimann Zeta-Function theory, one of the most important problems in analytic number theory. These results have application in solving problems in multiplicative number theory, such as power moments, the zero-free region, and the zero density estimates. The book also furnishes annotated proofs, end-of-chapter notes, historical discussions and references.

Contents

Elementary Theory; Exponential Integrals and Exponential Sums; The Voronoi Summation Formula; The Approximate Functional Equations; The Fourth Power Moment; The Zero-Free Region; Mean Value Estimates Over Short Intervals; Higher Power Moments; Omega Results; Zeros on the Critical Line; Zero-Density Estimates; The Distribution of Primes; The Dirichlet Divisor Problem; Various Other Divisor Problems; Atkinson's Formula for the Mean Square; Appendix; Author Index. Subject Index.