Average values of symmetric square <IMG >-functions at the edge of the critical strip期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Average values of symmetric square -functions at the edge of the critical strip

Authors:	J. Wu

Affiliation:	Institut Élie Cartan, UMR 7502 UHP-CNRS-INRIA, Université Henri Poincaré (Nancy 1), 54506 Vandouvre--lès--Nancy, France

Abstract:	Let ${mathcal{B}}_{2}^{}(N)$ be the set of all normalized newforms of weight 2 and level , and let $L({operatorname{sym}}^{2}f, 1)$ be the symmetric square -function associated to $fin {mathcal{B}}_{2}^{}(N)$ . If is a prime, then there is a positive constant such that $begin{displaymath}sum _{fin {mathcal{B}}_{2}^{*}(N)} L(1,{operatorname{sym}... ...{frac{pi ^{4}}{432}} N + Obig (N^{27/28} (log N)^{B}big ).end{displaymath}$ This improves a recent result of Akbary, which requires in place of .

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