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Paper detail

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

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.

preprint2019arXivOpen access
Han Wu
math.NT
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