Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory write by Solomon Friedberg. This book was released on 2006. Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory available in PDF, EPUB and Kindle. Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet
Multiple Dirichlet Series, L-functions and Automorphic Forms
Multiple Dirichlet Series, L-functions and Automorphic Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multiple Dirichlet Series, L-functions and Automorphic Forms write by Daniel Bump. This book was released on 2012-07-09. Multiple Dirichlet Series, L-functions and Automorphic Forms available in PDF, EPUB and Kindle. Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.
Number Theory, Analysis and Geometry
Number Theory, Analysis and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Number Theory, Analysis and Geometry write by Dorian Goldfeld. This book was released on 2011-12-20. Number Theory, Analysis and Geometry available in PDF, EPUB and Kindle. In honor of Serge Lang’s vast contribution to mathematics, this memorial volume presents articles by prominent mathematicians. Reflecting the breadth of Lang's own interests and accomplishments, these essays span the field of Number Theory, Analysis and Geometry.
Analytic Number Theory
Analytic Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic Number Theory write by William Duke. This book was released on 2007. Analytic Number Theory available in PDF, EPUB and Kindle. Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Gottingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of $L$-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Weyl Group Multiple Dirichlet Series
Weyl Group Multiple Dirichlet Series - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Weyl Group Multiple Dirichlet Series write by Ben Brubaker. This book was released on 2011-07-05. Weyl Group Multiple Dirichlet Series available in PDF, EPUB and Kindle. Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.
