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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Boston College, Chestnut Hill, MA, 02467-3806, USA

    Solomon Friedberg

  2. Department of Mathematics, Brown University, Providence, RI, 02912, USA

    Jeffrey Hoffstein

  3. Fidelity Capital Markets, 82 Devonshire St, Z2H, Boston, MA, 02109, USA

    Daniel Lieman

Authors
  1. Solomon Friedberg
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  2. Jeffrey Hoffstein
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  3. Daniel Lieman
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Correspondence to Solomon Friedberg.

Additional information

Mathematics Subject Classification (1991): 11R42, 11F66, 11F70, 11M41, 11R47.

Research supported in part by NSF grants DMS-9970118 (Friedberg), DMS-0088921 (Hoffstein), and DMS-9700542 (Lieman), and by NSA grant MDA 904-03-1-0012 (Friedberg).

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Friedberg, S., Hoffstein, J. & Lieman, D. Double Dirichlet series and the n-th order twists of Hecke L-series. Math. Ann. 327, 315–338 (2003). https://doi.org/10.1007/s00208-003-0455-4

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  • DOI: https://doi.org/10.1007/s00208-003-0455-4

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