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

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.

33 pages. Misprints are modified

References in corpus (1)

• Upper bounds on L-functions at the edge of the critical strip

Cited by in corpus (5)

• An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
• Weighted distribution of low-lying zeros of GL(2) L-functions
• A quantum probabilistic approach to Hecke algebras for $\mathfrak{p}$-adic ${\mathrm{PGL}}_2$
• Simple Fourier Trace Formulas of Cubic Level and Applications
• Hecke-Maass cusp forms on PGL_n of large levels with non-vanishing L-values