The Riemann Zeta-Function Theory and Applications

by Ivic, Aleksandar

• ISBN13: 9780486789019
• ISBN10: 0486789012
• Format: Hardcover
• Copyright: 2013-12-23
• Publisher: Dover Publications

Summary

"A thorough and easily accessible account." — MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estimates, the distribution of primes, the Dirichlet divisor problem and various other divisor problems, and Atkinson's formula for the mean square. End-of-chapter notes supply the history of each chapter's topic and allude to related results not covered by the book. 1985 edition.

Table of Contents

Notation
1. Elementary Theory
2. Exponential Integrals and Exponential Sums
3. The Voronoi Summation Formula
4. The Approximate Functional Equations
5. The Fourth Power Moment
6. The Zero-free Region
7. Mean Value Estimates Over Short Intervals
8. Higher Power Moments
9. Omega Results
10. Zeros on the Critical Line
11. Zero-density Estimates
12. The Distribution of Primes
13. The Dirichlet Divisor Problem
14. Various Other Divisor Problems
15. Atkinson's Formula for the Mean Square
Appendix. Indexes