Families of Automorphic Forms and the Trace Formula
Families of Automorphic Forms and the Trace Formula

Author: Werner Müller

Publisher: Springer

Published: 2016-09-20

Total Pages: 581

ISBN-13: 3319414240

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Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.

Random Matrices, Frobenius Eigenvalues, and Monodromy
Random Matrices, Frobenius Eigenvalues, and Monodromy

Author: Nicholas M. Katz

Publisher: American Mathematical Society

Published: 2023-11-13

Total Pages: 441

ISBN-13: 1470475073

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The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.

Applications of Random Matrices in Physics
Applications of Random Matrices in Physics

Author: Édouard Brezin

Publisher: Springer Science & Business Media

Published: 2006-03-03

Total Pages: 532

ISBN-13: 9781402045295

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Proceedings of the NATO Advanced Study Institute on Applications of Random Matrices in Physics, Les Houches, France, 6-25 June 2004

SCHOLAR -- a Scientific Celebration Highlighting Open Lines of Arithmetic Research
SCHOLAR -- a Scientific Celebration Highlighting Open Lines of Arithmetic Research

Author: A. C. Cojocaru

Publisher: American Mathematical Soc.

Published: 2015-12-22

Total Pages: 274

ISBN-13: 1470414570

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M. Ram Murty has had a profound impact on the development of number theory throughout the world. To honor his mathematical legacy, a conference focusing on new research directions in number theory inspired by his most significant achievements was held from October 15-17, 2013, at the Centre de Recherches Mathématiques in Montréal. This proceedings volume is representative of the broad spectrum of topics that were addressed at the conference, such as elliptic curves, function field arithmetic, Galois representations, -functions, modular forms and automorphic forms, sieve methods, and transcendental number theory. This book is co-published with the Centre de Recherches Mathématiques.

Mathematical Constants II
Mathematical Constants II

Author: Steven R. Finch

Publisher: Cambridge University Press

Published: 2003

Total Pages: 783

ISBN-13: 1108470599

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Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Women in Numbers 2
Women in Numbers 2

Author: Chantal David

Publisher: American Mathematical Soc.

Published: 2013-12-10

Total Pages: 218

ISBN-13: 1470410222

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The second Women in Numbers workshop (WIN2) was held November 6-11, 2011, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. During the workshop, group leaders presented open problems in various areas of number theory, and working groups tackled those problems in collaborations begun at the workshop and continuing long after. This volume collects articles written by participants of WIN2. Survey papers written by project leaders are designed to introduce areas of active research in number theory to advanced graduate students and recent PhDs. Original research articles by the project groups detail their work on the open problems tackled during and after WIN2. Other articles in this volume contain new research on related topics by women number theorists. The articles collected here encompass a wide range of topics in number theory including Galois representations, the Tamagawa number conjecture, arithmetic intersection formulas, Mahler measures, Newton polygons, the Dwork family, elliptic curves, cryptography, and supercongruences. WIN2 and this Proceedings volume are part of the Women in Numbers network, aimed at increasing the visibility of women researchers' contributions to number theory and at increasing the participation of women mathematicians in number theory and related fields. This book is co-published with the Centre de Recherches Mathématiques.