THE RIEMANN ZETA-FUNCTION: THEORY A

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.