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Trace formula and functional equation

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arxiv 2410.16921 v2 pith:AW7TQAFA submitted 2024-10-22 math.NT

Trace formula and functional equation

Chung-Hang Kwan , Wing Hong Leung This is my paper
classification math.NT
keywords equationformulafunctionalbeyond-endoscopiccuspformfunctionholomorphic
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We present a "beyond-endoscopic" treatment of the functional equation for the standard $L$-function of a holomorphic cusp form with level and nebentypus. We use Petersson's formula and methods from Venkatesh's thesis and "spectral reciprocity".

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  1. A trace formula derivation of the functional equation for symmetric square L-functions

    math.NT 2026-06 conditional novelty 6.0

    An averaged Voronoi-type identity from Petersson/Kuznetsov trace formulas recovers the classical functional equation of symmetric-square L-functions of level-one holomorphic and even Hecke–Maass forms.