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The Riemann Zeta-Function: Theory A: Theory and Applications by Aleksandar Ivic (Paperback, 2003)

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Notation 1. Exponential Integrals and Exponential Sums 3. The Voronoi Summation Formula 4. The Approximate Functional Equations 5. The Zero-free Region 7. Zeros on the Critical Line 11. Zero-density Estimates 12.

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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.