A generalized cubic moment and the Petersson formula for newforms

By Ian Petrow, M. Young. Mathematische Annalen, 2016

50 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c70e2721e3bae182bf1b42c84b8b19bd294b7fd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Ian Petrow
2. M. Young
3. E. M. Kıral
4. Siegfred Baluyot
5. Stephan Baier
6. Manjul Bhargava
7. A. Shankar
8. Alexandra Florea

In Applied Mathematics

1. Ian Petrow
2. M. Young
3. A. Shankar
4. Manjul Bhargava
5. Siegfred Baluyot

In Mathematical Physics

1. Ian Petrow
2. M. Young
3. E. M. Kıral
4. Alexandra Florea

Citations in the corpus

• Explicit calculations with Eisenstein series (2017, methodology): “icted to newforms, in the special case where the level is squarefree, the nebentypus is principal, and the weight is 0. This is an extension of the derivation of the Petersson formula for newforms of [PY], which proceeds by a sieving argument. The method of [PY] may be easily modified to sieve for cu”
• The Weyl bound for Dirichlet L-functions of cube-free conductor (2018, background): “al in [PY1, §10.4] to here. In that article, the analog of Kwas defined but with J±(x,·) replaced by J κ−1(x), the J-Bessel function, with κfixed. Nevertheless, a great majority of the work done on Kin [PY1] carries over to here, and the properties of J± developed in Section 10 will allow for this ext”
• The fourth moment of Dirichlet L-functions along a coset and the Weyl bound (2019, background): “[ILS] [PY2] [BM]), and it is not clear that there is any canonical choice for general level.”
• Oscillatory integrals with uniformity in parameters (2017, background): “in the analytic theory of L-functions [2], [7], [8].”