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arXiv · 1608.06854

A generalized cubic moment and the Petersson formula for newforms

Ian Petrow·Matthew P. Young
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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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Ian Petrow, Matthew P. Young. 2016-08-24. A generalized cubic moment and the Petersson formula for newforms. https://doi.org/10.1007/s00208-018-1745-1

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