Twisted moments of L-functions and spectral reciprocity

By V. Blomer, Rizwanur Khan. Duke mathematical journal, 2017

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A reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q twisted by the ell-th Hecke eigenvalue as the fourth moment of automorphic L-functions of level ell twisted by the q-th Hecke eigenvalue. Direct corollaries include subconvexity bounds for L-functions in the level aspect and a short proof of an upper bound for the fifth moment of automorphic L-functions.

Subfields: Algebra and Number Theory, Mathematical Physics

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