Mathematische Annalen

, Volume 327, Issue 2, pp 315–338

Double Dirichlet series and the n-th order twists of Hecke L-series

  • Solomon Friedberg
  • Jeffrey Hoffstein
  • Daniel Lieman

DOI: 10.1007/s00208-003-0455-4

Cite this article as:
Friedberg, S., Hoffstein, J. & Lieman, D. Math. Ann. (2003) 327: 315. doi:10.1007/s00208-003-0455-4


Let n≥3 be a fixed integer and let F be a global field containing the n-th roots of unity. In this paper we study the collective behavior of the n-th order twists of a fixed Hecke L-series for F. To do so, we introduce a double Dirichlet series in two complex variables (s, w) which is a weighted sum of the twists, and obtain its meromorphic continuation. We also study related sums of n-th order Gauss sums. These objects together satisfy a nonabelian group of functional equations in (s, w) of order 32.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Solomon Friedberg
    • 1
  • Jeffrey Hoffstein
    • 2
  • Daniel Lieman
    • 3
  1. 1.Department of MathematicsBoston CollegeUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA
  3. 3.Fidelity Capital MarketsBostonUSA