A Twisted Motohashi Formula and Weyl-Subconvexity for $L$-functions of Weight Two Cusp Forms

Ian Petrow

doi:10.1007/s00208-014-1166-8

A Twisted Motohashi Formula and Weyl-Subconvexity for $L$-functions of Weight Two Cusp Forms

Number Theory 2018-07-16 v3

Authors: Ian Petrow

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Abstract

We derive a Motohashi-type formula for the cubic moment of central values of $L$ -functions of level $q$ cusp forms twisted by quadratic characters of conductor $q$ , previously studied by Conrey and Iwaniec and Young. Corollaries of this formula include Weyl-subconvex bounds for $L$ -functions of weight two cusp forms twisted by quadratic characters, and estimates towards the Ramanujan-Petersson conjecture for Fourier coefficients of weight 3/2 cusp forms.

Keywords

Motohashi formula L-functions cusp forms Weyl-subconvexity quadratic characters Ramanujan-Petersson conjecture

Cite

@article{arxiv.1409.3524,
  title  = {A Twisted Motohashi Formula and Weyl-Subconvexity for $L$-functions of Weight Two Cusp Forms},
  author = {Ian Petrow},
  journal= {arXiv preprint arXiv:1409.3524},
  year   = {2018}
}

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