Exploring the Riemann Zeta function : 190 years from Riemann's birth

Description

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography. Front Matter ....Pages i-x An Introduction to Riemann’s Life, His Mathematics, and His Work on the Zeta Function (Roger Baker)....Pages 1-12 Ramanujan’s Formula for ζ(2n + 1) (Bruce C. Berndt, Armin Straub)....Pages 13-34 Towards a Fractal Cohomology: Spectra of Polya–Hilbert Operators, Regularized Determinants and Riemann Zeros (Tim Cobler, Michel L. Lapidus)....Pages 35-65 The Temptation of the Exceptional Characters (John B. Friedlander, Henryk Iwaniec)....Pages 67-81 Arthur’s Truncated Eisenstein Series for SL(2, Z) and the Riemann Zeta Function: A Survey (Dorian Goldfeld)....Pages 83-97 On a Cubic Moment of Hardy’s Function with a Shift (Aleksandar Ivić)....Pages 99-112 Some Analogues of Pair Correlation of Zeta Zeros (Yunus Karabulut, Cem Yalçın Yıldırım)....Pages 113-179 Bagchi’s Theorem for Families of Automorphic Forms (E. Kowalski)....Pages 181-199 The Liouville Function and the Riemann Hypothesis (Michael J. Mossinghoff, Timothy S. Trudgian)....Pages 201-221 Explorations in the Theory of Partition Zeta Functions (Ken Ono, Larry Rolen, Robert Schneider)....Pages 223-264 Reading Riemann (S. J. Patterson)....Pages 265-285 A Taniyama Product for the Riemann Zeta Function (David E. Rohrlich)....Pages 287-298