Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)
Masao Tsuzuki, "Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)"
English | ISBN: 1470410192 | 2015 | 129 pages | PDF | 1 MB
English | ISBN: 1470410192 | 2015 | 129 pages | PDF | 1 MB
Starting with Green's functions on adele points of $\mathrm{GL}(2)$ considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central $L$-values attached to cuspidal waveforms with square-free level.