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Exploring the Riemann Zeta Function

190 years from Riemann's Birth

  • Book
  • © 2017

Overview

Editors:
  1. Hugh Montgomery

    1. Department of Mathematics, University of Michigan, Ann Arbor, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Ashkan Nikeghbali

    1. Institut für Mathematik, Universität Zürich, Zürich, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

  3. Michael Th. Rassias

    1. Institut für Mathematik, Universität Zürich, Zürich, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

  • 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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. An Introduction to Riemann’s Life, His Mathematics, and His Work on the Zeta Function

    • Roger Baker
    Pages 1-12

  3. Ramanujan’s Formula for ζ(2n + 1)

    • Bruce C. Berndt, Armin Straub
    Pages 13-34

  4. Towards a Fractal Cohomology: Spectra of Polya–Hilbert Operators, Regularized Determinants and Riemann Zeros

    • Tim Cobler, Michel L. Lapidus
    Pages 35-65

  5. The Temptation of the Exceptional Characters

    • John B. Friedlander, Henryk Iwaniec
    Pages 67-81

  6. Arthur’s Truncated Eisenstein Series for SL(2, Z) and the Riemann Zeta Function: A Survey

    • Dorian Goldfeld
    Pages 83-97

  7. On a Cubic Moment of Hardy’s Function with a Shift

    • Aleksandar Ivić
    Pages 99-112

  8. Some Analogues of Pair Correlation of Zeta Zeros

    • Yunus Karabulut, Cem Yalçın Yıldırım
    Pages 113-179

  9. Bagchi’s Theorem for Families of Automorphic Forms

    • E. Kowalski
    Pages 181-199

  10. The Liouville Function and the Riemann Hypothesis

    • Michael J. Mossinghoff, Timothy S. Trudgian
    Pages 201-221

  11. Explorations in the Theory of Partition Zeta Functions

    • Ken Ono, Larry Rolen, Robert Schneider
    Pages 223-264

  12. Reading Riemann

    • S. J. Patterson
    Pages 265-285

  13. A Taniyama Product for the Riemann Zeta Function

    • David E. Rohrlich
    Pages 287-298
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Keywords

About this book

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.

Reviews

“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)

Editors and Affiliations

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Hugh Montgomery

  • Institut für Mathematik, Universität Zürich, Zürich, Switzerland

    Ashkan Nikeghbali, Michael Th. Rassias

About the editors

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.



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