A note on the second moment of automorphic L-functions

Abstract

We obtain the formula for the twisted harmonic second moment of the $L$-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean value theorem is reminiscent of recent results of Conrey and Young on the reciprocity formula for the twisted second moment of Dirichlet $L$-functions.

9 pages

Cited by in corpus (3)

• On the reciprocity law for the twisted second moment of Dirichlet $L$-functions
• Asymptotic formulas for the second moments of $L$-series associated to holomorphic cusp forms on the critical line
• Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions