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Deducing Selberg trace formula via Rankin–Selberg method for ????????₂
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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.
Title: Deducing Selberg trace formula via Rankin–Selberg method for ????????₂
Description:
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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