Geodesic
The first moment of central values of symmetric square $L$-functions of cusp forms
Ming-Ho Ng1
1 Department of of Mathematics The University of Hong Kong Pokfulam Road, Hong Kong
Acta Arithmetica, Tome 177 (2017) no. 3, pp. 277-291

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Asymptotic formulae for the twisted first moment of central values of symmetric square $L$-functions with harmonic weight in the weight aspect are obtained. The result extends some results in the literature. It is applied to derive an asymptotic formula for the first moment of central values of symmetric square $L$-functions without harmonic weight, under the assumption that the $L$-function is non-negative at the center of the critical strip. Analogous new formulae without harmonic weight for the first and second moments of Hecke $L$-functions are proved.
DOI : 10.4064/aa8382-8-2016
Keywords: asymptotic formulae twisted first moment central values symmetric square l functions harmonic weight weight aspect obtained result extends results literature applied derive asymptotic formula first moment central values symmetric square l functions without harmonic weight under assumption l function non negative center critical strip analogous formulae without harmonic weight first second moments hecke l functions proved

Ming-Ho Ng 1

1 Department of of Mathematics The University of Hong Kong Pokfulam Road, Hong Kong 
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Ming-Ho Ng. The first moment of central values of symmetric square $L$-functions of cusp forms. Acta Arithmetica, Tome 177 (2017) no. 3, pp. 277-291. doi: 10.4064/aa8382-8-2016

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