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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Deducing Selberg trace formula via Rankin-Selberg method for $ {GL}_2$

Author: Han Wu
Journal: Trans. Amer. Math. Soc. 372 (2019), 8507-8551
MSC (2010): Primary 11F72; Secondary 11F70
Published electronically: June 3, 2019
MathSciNet review: 4029703
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Abstract: In the 1980s, Zagier and Jacquet and Zagier tried to derive the Selberg trace formula by applying the Rankin-Selberg method to the automorphic kernel function. Their derivation was incomplete due to a puzzle of the computation of a residue. We solve this puzzle and complete the derivation. The main input is an extension of the theory of regularized integrals invented by Zagier, which is of independent interest.

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Additional Information

Han Wu
Affiliation: EPFL SB MATHGEOM TAN, MA C3 604, Station 8, CH-1015 Lausanne, Switzerland

Received by editor(s): October 27, 2018
Received by editor(s) in revised form: February 23, 2019, and March 18, 2019
Published electronically: June 3, 2019
Additional Notes: The preparation of the paper scattered during the stays of the author in FIM at ETHZ, YMSC at Tsinghua University, Alfréd Renyi Institute in Hungary supported by the MTA Rényi Intézet Lendület Automorphic Research Group, and TAN at EPFL. The author would like to thank all of these institutes for their hospitality.
Article copyright: © Copyright 2019 American Mathematical Society