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Random matrices and number theory: some recent themes

Jon P. Keating

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and ... More


Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Ben Brubaker, Daniel Bump, and Solomon Friedberg

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

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, ... More


From Abel-Poisson to Bochner-Riesz Summability

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 1 - Classical Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733133
eISBN:
9780191797712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733133.003.0011
Subject:
Mathematics, Analysis

This chapter begins with an introduction of Fourier transform on ℝn and then covers various summability methods including Abel-Poisson, Gauss-Weierstrass and later Bochner-Riesz. It also discusses ... More


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