The first moment of cusp form -functions in weight aspect on average
Tom 181 / 2017
Acta Arithmetica 181 (2017), 197-208
MSC: Primary 11F11.
DOI: 10.4064/aa8569-8-2017
Opublikowany online: 20 November 2017
Streszczenie
We prove an asymptotic formula for the twisted first moment of central L-values in weight aspect on average. Our estimate of the error term allows extending the logarithmic length of the mollifier \Delta up to 2. The best previously known result, due to Iwaniec and Sarnak, was \Delta \lt 1. The proof is based on a representation formula for the error in terms of Legendre polynomials.
