The first moment of cusp form L-functions in weight aspect on average
Balkanova, Olga · Frolenkov, Dmitry
الأصل · EN
We study the asymptotic behaviour of the twisted first moment of central L-values associated to cusp forms in weight aspect on average. Our estimate of the error term allows extending the logarithmic length of mollifier Δ up to 2. The best previously known result, due to Iwaniec and Sarnak, was Δ<1. The proof is based on a representation formula for the error in terms of Legendre polynomials.
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