Volume 26 - 2003

1. Mean-square upper bound of Hecke $L$-functions on the critical line.

We prove the upper bound for the mean-square of the absolute value of the Hecke $L$-functions (attached to a holomorphic cusp form) defined for the congruence subgroup $\Gamma_0 (N)$ on the critical line uniformly with respect to its conductor $N$.