Exploring the Riemann Zeta Function

190 years from Riemann's Birth
Softcover Nachdruck of the original 1. Auflage 2017
ISBN: 978-3-319-86748-9
Verlag: Springer International Publishing

Buch, Englisch, 298 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 470 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Montgomery, Hugh

Rassias, Michael Th.

Nikeghbali, Ashkan

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Nichtlineare Wissenschaft
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

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. Yildirim).- 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. Rohrlichll).

Über Autor(innen)

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.