The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions PDF Download

Author: Valentin Blomer
Publisher: American Mathematical Society
ISBN: 1470456788
Category : Mathematics
Languages : en
Pages : 160

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Author: Michael Rosen
Publisher: Springer Science & Business Media
ISBN: 1475760469
Category : Mathematics
Languages : en
Pages : 355

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Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.

Author: D. Bump
Publisher: Springer
ISBN: 3540390553
Category : Mathematics
Languages : en
Pages : 196

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Author: Sarvadaman Chowla
Publisher: CRC Press
ISBN: 9780677001401
Category : Mathematics
Languages : en
Pages : 144

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Author: H. Iwaniec
Publisher: American Mathematical Society
ISBN: 1470418517
Category : Mathematics
Languages : en
Pages : 130

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The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. There are also technical lemmas which can be useful in a broader context.

Author: J. B. Conrey
Publisher: Cambridge University Press
ISBN: 0521699649
Category : Mathematics
Languages : en
Pages : 5

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This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.

Author: Anatoly A. Karatsuba
Publisher: Walter de Gruyter
ISBN: 3110886146
Category : Mathematics
Languages : en
Pages : 409

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author: Noga Alon
Publisher: Birkhäuser
ISBN: 9783034604246
Category : Mathematics
Languages : en
Pages : 528

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"Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a two-volume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future.

Author: Dennis A. Hejhal
Publisher: Springer Science & Business Media
ISBN: 9780387988245
Category : Mathematics
Languages : en
Pages : 716

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Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Author: Roger Godement
Publisher: Springer
ISBN: 3540374361
Category : Mathematics
Languages : en
Pages : 200

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