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Mathematische Annalen

, Volume 373, Issue 1–2, pp 287–353 | Cite as

A generalized cubic moment and the Petersson formula for newforms

  • Ian PetrowEmail author
  • Matthew P. Young
Article

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.

Mathematics Subject Classification

11F11 11F37 11F66 11M99 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsETH ZürichZurichSwitzerland
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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