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Summary:

This book is concerned with the Riemann Zeta Function, its generalizations, and various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis and Probability Theory. Eminent experts in the field illustrate both old and new results towards the solution of long-standing problems and include key historical remarks. Offering a unified, self-contained treatment of broad and deep areas of research, this book will be an excellent tool for researchers and graduate students working in Mathematics, Mathematical Physics, Engineering and Cryptography.

Table of Contents:

• Preface by Freeman J. Dyson: Quasi-crystals and the Riemann hypothesis
• An introduction to Riemann's life, his mathematics, and his work on the zeta function / Roger Baker
• Ramanujan's formula ... / Bruce C. Berndt and Armin Straub
• Towards a fractal cohomology: spectra of polya-Hilbert operators, regularized determinants and Riemann zeros / Tim Cobler and Michel L. Lapidus
• The temptation of the exceptional characters / John B. Friedlander and Henryk Iwaniec
• Arthur's truncated Eisenstein series for SL(2, Z) and the Riemann zeta function: a survey / Dorian Goldfield
• On a cubic moment of Hardy's function with a shift / Aleksandar Ivić
• Some analogues of pair correlation of zeta zeros
• Yunus Karabulut and Çem Yalcin ̧Yıldırım
• Bagchi's theorem for families of automorphic forms
• E. Kowalski
• The Liouville function and the Riemann hypothesis / Michael J. Mossinghoff and Timothy S. Trudgians
• Explorations in the theory of partition zeta functions / Ken Ono, Larry Rolen, and Robert Schneider
• Reading Riemann / S.J. Patterson
• A Taniyama product for the Riemann zeta function / David E. Rohrlich.

Contributors:

Montgomery, Hugh L. , editor

Nikeghbali, Ashkan, 1975- , editor

Rassias, Michael Th., 1987- , editor

Languages:

English

Language Notes:

Item content: English

Subjects:

Reimann, Bernhard, 1826-1866

Riemann hypothesis

Functions, Zeta

Difference equations

Functional equations

Ergodic theory

Functions of complex variables

General Notes:

Description based on: Print version record.

Physical Description:

1 online resource (x, 298 pages)

Digital Characteristics:

text file

Call Numbers:

QA351 .E975 2017eb

ISBNs:

9783319599694
3319599690
9783319599687 (print) [Invalid]
3319599682 [Invalid]

Other Standard Numbers:

Digital Object Identifier: 10.1007/978-3-319-59969-4

OCLC Numbers:

1021277106