Distribution of mass of holomorphic cusp forms
By V. Blomer, Rizwanur Khan, M. Young. 2012
182 citations recorded by the source corpus.
We prove an upper bound for the L^4-norm and for the L^2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form of large weight. The method is based on Watson's formula and estimating a mean value of certain L-functions of degree 6. Further applications to restriction problems of Siegel modular forms and subconvexity bounds of degree 8 L-functions are given.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fe9f44eb961dfc41f835da2fcec722872f755267
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
- Ian Petrow
- M. Young
- E. M. Kıral
- Siegfred Baluyot
- Stephan Baier
- Manjul Bhargava
- A. Shankar
- Alexandra Florea
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A generalized cubic moment and the Petersson formula for newforms (2016, methodology): “tegration by parts. Often an integral can be shown to be small by repeated integration by parts. For this, we quote [BKY, Lemma 8.1] with some slight changes of notation and terminology. Lemma 10.2 ( [BKY]). Suppose that w = wT(t) is a family of X-inert functions, with compact support on [Z,2Z], so ”
- Weyl-type hybrid subconvexity bounds for twisted $L$-functions and Heegner points on shrinking sets (2014, methodology): “then this error term is not much smaller than the main term, and we cannot apply savings in the q-aspect on the error term from the T-aspect. For this reason, we will quote some convenient results of [BKY] that have sufficiently strong errors. First we begin with a useful definition. Definition 6.1. Sup”
- Oscillatory integrals with uniformity in parameters (2017, methodology): “To continue this discussion, we synthesize Lemma 8.1 and Proposition 8.2 of [1] using this language of inert functions, along with some simplified choices of parameters, with the following: Lemma 3.1 ([1]). Suppose that w = wT(t) is a family of X-inert functions, with compact support on [Z,2Z], so th”