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

• Autores: J. Hoffstein, S. Friedberg
• Localización: Mathematische Annalen, ISSN 0025-5831, Vol. 327, Nº 2, 2003, pág. 315
• Idioma: inglés
• DOI: 10.1007/s00208-003-0455-4
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• Resumen

  • 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.