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A generalized cubic moment and the Petersson formula for newforms

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Abstract

Using a cubic moment, we prove a Weyl-type subconvexity bound for the quadratic twists of a holomorphic newform of square-free level, trivial nebentypus, and arbitrary even weight. This generalizes work of Conrey and Iwaniec in that the newform that is being twisted may have arbitrary square-free level, and also that the quadratic character may have even conductor. One of the new tools developed in this paper is a more general Petersson formula for newforms of square-free level.

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Notes

  1. This corrects a claimed formula for \(g(\chi _q, \psi _0)\) of [14, p.1212].

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Authors and Affiliations

  1. Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092, Zurich, Switzerland

    Ian Petrow

  2. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Matthew P. Young

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  1. Ian Petrow
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Correspondence to Ian Petrow.

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Communicated by Kannan Soundararajan.

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Petrow, I., Young, M.P. A generalized cubic moment and the Petersson formula for newforms. Math. Ann. 373, 287–353 (2019). https://doi.org/10.1007/s00208-018-1745-1

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