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arXiv · 1810.09437

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

Han Wu
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Abstract

In the 80s, Zagier and Jacquet-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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Han Wu. 2018-10-20. Deducing Selberg trace formula via Rankin-Selberg method for $\mathrm{GL}_2$. https://doi.org/10.1090/tran%2F7853

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