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AVERAGES OF TWISTED $L$ -FUNCTIONS

Published online by Cambridge University Press:  24 June 2015

JULIA JACKSON
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019-3103, USA email j.jackson@ou.edu
ANDREW KNIGHTLY
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, USA email knightly@math.umaine.edu
Corresponding
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Abstract

We use a relative trace formula on $\text{GL}(2)$ to compute a sum of twisted modular $L$ -functions anywhere in the critical strip, weighted by a Fourier coefficient and a Hecke eigenvalue. When the weight $k$ or level $N$ is sufficiently large, the sum is nonzero. Specializing to the central point, we show in some cases that the resulting bound for the average is as good as that predicted by the Lindelöf hypothesis in the $k$ and $N$ aspects.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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