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arXiv · 2405.02998

Zeroes of Rankin-Selberg $L$-functions and the trace formula

Tian An Wong
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Abstract

We express the contribution of certain maximal parabolic Eisenstein series to the spectral side of the Arthur--Selberg trace formula for GL$(n)$ in terms of zeroes of Rankin--Selberg $L$-functions, generalizing previous results for GL(2) and Hecke $L$-functions. As applications, we prove a lower bound for the sum of these zeroes, and a base change relation between the zeroes in the case $n=2$ for cyclic extensions of prime degree.

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Tian An Wong. 2024-05-05. Zeroes of Rankin-Selberg $L$-functions and the trace formula. https://arxiv.org/abs/2405.02998

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