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Journal of the Ramanujan Mathematical Society

Volume 38, Issue 4, December 2023  pp. 393–403.

Zeroes of Rankin–Selberg L–functions and the trace formula

Authors:  Tian An Wong
Author institution: University of Michigan-Dearborn, 4901 Evergreen Road, Dearborn, MI 48128, USA.

Summary:  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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