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The shifted fourth moment of automorphic $L$-functions of prime power level

Volume 174 / 2016

Olga Balkanova Acta Arithmetica 174 (2016), 121-174 MSC: Primary 11F67, 11F11; Secondary 11M50. DOI: 10.4064/aa8165-4-2016 Published online: 4 July 2016


We prove an asymptotic formula for the fourth moment of automorphic $L$-functions of level $p^{\nu }$, where $p$ is a fixed prime number and $\nu \rightarrow \infty $. This is a continuation of work by Rouymi, who computed the asymptotics of the first three moments at a prime power level, and a generalization of results obtained for a prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & VanderKam.


  • Olga BalkanovaInstitut de Mathématiques de Bordeaux
    Université de Bordeaux
    351 cours de la Liberation
    33405 Talence Cedex, France

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