Vol. 260, No. 2, 2012

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Modular L-values of cubic level

Andrew Knightly and Charles Li

Vol. 260 (2012), No. 2, 527–563
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Using a simple relative trace formula, we compute averages of twisted modular L-values for newforms of cubic level. In the case of Maass forms, we obtain an exact formula. For holomorphic forms of weight k > 2, we obtain an asymptotic formula, which agrees with the estimate predicted by the Lindelöf hypothesis in the weight and level aspects.

L-functions, relative trace formula, supercuspidal representations, Maass forms
Mathematical Subject Classification 2010
Primary: 11
Secondary: 11F41, 11F70, 11F72
Received: 13 July 2012
Accepted: 4 October 2012
Published: 30 November 2012
Andrew Knightly
Department of Mathematics and Statistics
University of Maine
5752 Neville Hall, Rm 333
Orono ME 04469-5752
United States
Charles Li
Department of Mathematics
The Chinese University of Hong Kong
Room 218
Lady Shaw Building
Hong Kong