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

Abstract : 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 $N$.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01109810
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Submitted on : Tuesday, January 27, 2015 - 9:45:17 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Tuesday, April 28, 2015 - 10:12:09 AM

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26Article1.pdf
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### Citation

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

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