Exploring the Riemann Zeta Function

1. Front Matter

   Pages i-x

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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

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.

• analytic number theory
• probability theory
• ergodic theory
• harmonic analysis
• approximation theory
• special functions

“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)

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

  Hugh Montgomery

• Institut für Mathematik, Universität Zürich, Zürich, Switzerland

  Ashkan Nikeghbali, Michael Th. Rassias

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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