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Exploring the Riemann Zeta Function: 190 years from Riemann's Birth de Hugh Montgomery

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

Editat de Hugh Montgomery, Ashkan Nikeghbali, Michael Th. Rassias
en Limba Engleză Hardback – 18 sep 2017
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.
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Specificații

ISBN-13: 9783319599687
ISBN-10: 3319599682
Pagini: 272
Ilustrații: X, 298 p. 7 illus., 5 illus. in color.
Dimensiuni: 155 x 235 x 24 mm
Greutate: 5.86 kg
Ediția:1st ed. 2017
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

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).

Recenzii

“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)

Notă biografică

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.


Textul de pe ultima copertă

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.

Caracteristici

Illustrates mathematical results and solves open problems in a simple manner
Features contributions by experts in analysis, number theory, and related fields
Contains new results in rapidly progressing areas of research