Abstract
We study the first moment of symmetric-square -functions at the critical point in the weight aspect. Asymptotics with the best known error term were obtained independently by Fomenko in 2003 and by Sun in 2013. We prove that there is an extra main term of size in the asymptotic formula and show that the remainder term decays exponentially in . The twisted first moment was evaluated asymptotically by Ng with the error bounded by . We improve the error bound to unconditionally and to under the Lindelöf hypothesis for quadratic Dirichlet -functions.
Citation
Olga Balkanova. Dmitry Frolenkov. "The mean value of symmetric square $L$-functions." Algebra Number Theory 12 (1) 35 - 59, 2018. https://doi.org/10.2140/ant.2018.12.35
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