## A Sankaranarayanan - Mean-square upper bound of Hecke $L$-functions on the critical line.

hrj:147 - Hardy-Ramanujan Journal, January 1, 2003, Volume 26 - https://doi.org/10.46298/hrj.2003.147
Mean-square upper bound of Hecke $L$-functions on the critical line.

Authors: A Sankaranarayanan

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 $N$.

Volume: Volume 26
Published on: January 1, 2003
Submitted on: March 3, 2015
Keywords: Holomorphic cusp forms, Mean-value theorems, Montgomery-Vaughan Theorem,Hecke $L$-functions,[MATH] Mathematics [math]

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