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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