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arXiv · 1906.01172

Spectral average of central values of automorphic L-functions for holomorphic cusp forms on SO_0(m,2) II

Masao Tsuzuki
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Abstract

Given a maximal even-integral lattice $\cL$ of signature $(m+, 2-)$ with an odd $m\geq 3$, we consider the holomorphic cusp forms $F$ of weight $l$ on the bounded symmetric domain of type IV of dimension $m$ with respect to the discriminant subgroup of the orthogonal group $O(\cL)$ defined by $\cL$. Under a non-negativity assumption on the central $L$-values, we prove an equidistribution result of Satake parameters in an ensemble constructed from the central values of standard $L$-functions and the square of the Whittaker-Bessel periods.

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Masao Tsuzuki. 2019-06-04. Spectral average of central values of automorphic L-functions for holomorphic cusp forms on SO_0(m,2) II. https://arxiv.org/abs/1906.01172

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