The first moment of cusp form L-functions in weight aspect on average
Abstract
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 up to 2. The best previously known result, due to Iwaniec and Sarnak, was <1. The proof is based on a representation formula for the error in terms of Legendre polynomials.
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