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• W3100314986 abstract "This paper studies the first moment of symmetric-square $L$-functions at the critical point in the weight aspect. Asymptotics with the best known error term $O(k^{-1/2})$ were obtained independently by Fomenko in 2005 and by Sun in 2013. We prove that there is an extra main term of size $k^{-1/2}$ in the asymptotic formula and show that the remainder term decays exponentially in $k$. The twisted first moment was evaluated asymptotically by Ng Ming Ho with the error bounded by $lk^{-1/2+epsilon}$. We improve the error bound to $l^{5/6+epsilon}k^{-1/2+epsilon}$ unconditionally and to $l^{1/2+epsilon}k^{-1/2}$ under the Lindel{o}f hypothesis for quadratic Dirichlet $L$-functions." @default.
• W3100314986 created "2020-11-23" @default.
• W3100314986 creator A5048625658 @default.
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• W3100314986 date "2018-03-13" @default.
• W3100314986 modified "2023-10-14" @default.
• W3100314986 title "The mean value of symmetric square L-functions" @default.
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• W3100314986 doi "https://doi.org/10.2140/ant.2018.12.35" @default.
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