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Multiple Dirichlet Series, L-functions and Automorphic Forms pp 1–36Cite as

Birkhäuser

Introduction: Multiple Dirichlet Series

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Part of the book series: Progress in Mathematics ((PM,volume 300))

Abstract

This introductory article aims to provide a roadmap to many of the interrelated papers in this volume and to a portion of the field of multiple Dirichlet series, particularly emerging new ideas. It is both a survey of the recent literature, and an introduction to the combinatorial aspects of Weyl group multiple Dirichlet series, a class of multiple Dirichlet series that are not Euler products, but which may nevertheless be reconstructed from their p-parts. These p-parts are combinatorially interesting, and may often be identified with p-adic Whittaker functions.

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Notes

  1. 1.

    If \(\hat{G}\)is semisimple, then the root lattice has finite index in Λ.

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  1. Department of Mathematics, Stanford University, Stanford, CA, 94305-2125, USA

    Daniel Bump

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Correspondence to Daniel Bump .

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  1. Department of Mathematics, Stanford University, Stanford, 94305-2125, California, USA

    Daniel Bump

  2. , Department of Mathematics, Boston College, Commonwealth Ave. 140, Chestnut Hill, 02467-3806, Massachusetts, USA

    Solomon Friedberg

  3. , Department of Mathematics, Columbia University, Broadway 2990, New York, 10027, New York, USA

    Dorian Goldfeld

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Bump, D. (2012). Introduction: Multiple Dirichlet Series. In: Bump, D., Friedberg, S., Goldfeld, D. (eds) Multiple Dirichlet Series, L-functions and Automorphic Forms. Progress in Mathematics, vol 300. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8334-4_1

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