Exploring the Riemann Zeta Function: 190 Years from Riemann's Birth

ISBN-13: 9783319867489 / Angielski / Miękka / 2018 / 298 str.

Hugh Montgomery; Ashkan Nikeghbali; Michael Th Rassias

Recenzje

"The best thing in this book that it contains a wide range of information which opens a lot of doors for researchers. It is good to have these formidable results in one book. ... Riemann's zeta function is difficult to understand deeply, but this book is a very good help to reach that goal." (Salim Salem, MAA Reviews, February, 2018)

Spis treści

Preface (Dyson).- 1. An introduction to Riemann's life, his mathematics, and his work on the zeta function (R. Baker).- 2. Ramanujan's formula for zeta (2n+1) (B.C. Berndt, A. Straub).- 3. Towards a fractal cohomology: Spectra of Polya-Hilbert operators, regularized determinants, and Riemann zeros (T. Cobler, M.L. Lapidus).- The Temptation of the Exceptional Characters (J.B. Friedlander, H. Iwaniec).- 4. The Temptation of the Exceptional Characters (J.B. Friedlander, H. Iwaniec).- 5. Arthur's truncated Eisenstein series for SL(2,Z) and the Riemann Zeta Function, A Survey (D. Goldfield).- 6. On a Cubic moment of Hardy's function with a shift (A. Ivic).- 7. Some analogues of pair correlation of Zeta Zeros (Y. Karabulut, C.Y. Yıldırım).- 8. Bagchi's Theorem for families of automorphic forms (E. Kowalski).- 9. The Liouville function and the Riemann hypothesis (M.J. Mossinghoff, T.S. Trudgian).- 10. Explorations in the theory of partition zeta functions (K. Ono, L. Rolen, R. Schneider).- 11. Reading Riemann (S.J. Patterson).- 12. A Taniyama product for the Riemann zeta function (D.E. Rohrlichłł).

O autorze

Michael Th. Rassias is a Postdoctoral researcher at the Institute of Mathematics of the University of Zürich and a visiting researcher at the Program in Interdisciplinary Studies of the Institute for Advanced Study, Princeton.

Blurb

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.