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

Ben Brubaker, Daniel Bump, and Solomon Friedberg

Abstract

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 an ... More

Keywords: functional equation, Riemann zeta function, analytic continuation, analytic number theory, Weyl group multiple Dirichlet series, Euler product, Whittaker coefficient, Kashiwara's crystal, Yang–Baxter equation, Weyl character formula

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780691150659
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691150659.001.0001

Authors

Affiliations are at time of print publication.

Ben Brubaker, author
Massachusetts Institute of Technology

Daniel Bump, author
Stanford University

Solomon Friedberg, author
Boston College