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arXiv · 1312.2732

Asymptotic behaviors of means of central values of automorphic $L$-functions for GL(2)

Shingo Sugiyama
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Abstract

Let $\mathbb{A}$ be the adele ring of a totally real algebraic number field $F$. We push forward an explicit computation of a relative trace formula for periods of automorphic forms along a split torus in $GL(2)$ from a square free level case done by Masao Tsuzuki, to an arbitrary level case. By using a relative trace formula, we study central values of automorphic $L$-functions for cuspidal automorphic representations of $GL(2, \mathbb{A})$ corresponding to Maass forms with arbitrary level.

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BibTeXRIS

Shingo Sugiyama. 2013-12-10. Asymptotic behaviors of means of central values of automorphic $L$-functions for GL(2). https://doi.org/10.1016/j.jnt.2015.04.003

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