The Riemann Zeta-function Theory and Applications
The Riemann Zeta-function Theory and Applications by A. Ivi is a comprehensive exploration of Riemann zeta-function theory and its applications, published by Courier Corporation in 2003. This reprint edition spans 517 pages and is presented in English. The book begins with elementary theory and progresses through various advanced topics, including exponential integrals, the Voronoi summation formula, and the distribution of primes.
Readers will find a thorough examination of significant concepts such as the zero-density estimates and the Dirichlet divisor problem. The text also includes end-of-chapter notes that provide historical context and references to related results not covered within the main content. This extensive survey is designed to be accessible while delving into complex mathematical topics, making it a valuable resource for those interested in mathematics, functional analysis, and complex analysis.
Official synopsis Publisher
“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.
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