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

A Sankaranarayanan (1)

1 TIFR - Tata Institute for Fundamental Research

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 $N$.

Mots clés: Hecke $L$-functions; Holomorphic cusp forms; Mean-value theorems; Montgomery-Vaughan Theorem

Domaines: Mathématiques [math]

A Sankaranarayanan. Mean-square upper bound of Hecke $L$-functions on the critical line.. Hardy-Ramanujan Journal, 2003, Volume 26 - 2003, pp.2-17. ⟨10.46298/hrj.2003.147⟩. ⟨hal-01109810⟩