Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)(English, Paperback, Tsuzuki Masao) | Zipri.in
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Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)(English, Paperback, Tsuzuki Masao)

Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)(English, Paperback, Tsuzuki Masao)

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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.