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**About this book :- **
**Exploring the Riemann Zeta Function ** written by
** Hugh Montgomery, Ashkan Nikeghbali, Michael Rassias **.

There were until recently two supreme unsolved problems in the world of pure mathematics, the proof of Fermat’s Last Theorem and the proof of the Riemann Hypothesis. In 1998, my former Princeton colleague Andrew Wiles polished off Fermat’s Last Theorem, and only the Riemann Hypothesis remains. Wiles’ proof of the Fermat Theorem was not just a technical stunt. It required the discovery and exploration of a new field of mathematical ideas, far wider and more consequential than the Fermat Theorem itself. It is likely that any proof of the Riemann Hypothesis will likewise lead to a deeper understanding of many diverse areas of mathematics and perhaps of physics too. The Riemann Hypothesis says that one specific function, the zeta-function that Riemann named, has all its complex zeros upon a certain line. Riemann’s zeta-function and other zeta-functions similar to it appear ubiquitously in number theory, in the theory of dynamical systems, in geometry, in function theory, and in physics. The zeta-function stands at a junction where paths lead in many directions.

**Book Detail :- **
** Title: ** Exploring the Riemann Zeta Function
** Edition: **
** Author(s): ** Hugh Montgomery, Ashkan Nikeghbali, Michael Rassias
** Publisher: ** Springer
** Series: **
** Year: ** 2017
** Pages: ** 300
** Type: ** PDF
** Language: ** English
** ISBN: ** 3319599682,9783319599687
** Country: ** US
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**About Author :- **
The author ** Hugh Lowell Montgomery ** (born, 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis. As a Marshall scholar, Montgomery earned his Ph.D. from the University of Cambridge. For many years, Montgomery has been teaching at the University of Michigan.

He is best known for Montgomery's pair correlation conjecture, his development of the large sieve methods and for co-authoring (with Ivan M. Niven and Herbert Zuckerman) one of the standard introductory number theory texts, An Introduction to the Theory of Numbers, now in its fifth edition (ISBN 0471625469). In 2012 he became a fellow of the American Mathematical Society.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Exploring the Riemann Zeta Function by Hugh Montgomery, Ashkan Nikeghbali, Michael Rassias **

** • Download PDF Early Fourier Analysis by Hugh L. Montgomery **

** • Download PDF Topics in Multiplicative Number Theory by Hugh L. Montgomery **

** • Download PDF Multiplicative Number Theory I: Classical Theory by Hugh L. Montgomery, Robert C. Vaughan **

** • Download PDF Interface between Analytic Number Theory & Harmonic Analysis by Hugh L. Montgomery **

** • Download PDF An Introduction to the Theory of Numbers, 5E by Ivan Niven, Herbert Zuckerman, Hugh Montgomery **

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**Book Contents :- **
**Exploring the Riemann Zeta Function ** written by
** Hugh Montgomery, Ashkan Nikeghbali, Michael Rassias **
cover the following topics.
'

Preface by Freeman J. Dyson:

Quasi-Crystals and the Riemann Hypothesis

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

Ramanujan’s Formula for (2n C 1), Bruce C. Berndt, Armin Straub

Towards a Fractal Cohomology: Spectra of Polya–Hilbert Operators, Regularized Determinants and Riemann Zeros, Tim Cobler, Michel L. Lapidus

The Temptation of the Exceptional Characters, John B. Friedlander, Henryk Iwaniec

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

On a Cubic Moment of Hardy’s Function with a Shift, Aleksandar Ivi´c

Some Analogues of Pair Correlation of Zeta Zeros, Yunus Karabulut, Cem Yalçın Yıldırım

Bagchi’s Theorem for Families of Automorphic Forms, E. Kowalski

The Liouville Function and the Riemann Hypothesis, Michael J. Mossinghoff, Timothy S. Trudgian

Explorations in the Theory of Partition Zeta Functions, Ken Ono, Larry Rolen, Robert Schneider

Reading Riemann, S.J. Patterson

A Taniyama Product for the Riemann Zeta Function, David E. Rohrlich

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