Bounding sup-norms of cusp forms of large level
By V. Blomer, R. Holowinsky. 2008
79 citations recorded by the source corpus.
Let f be an L2-normalized weight zero Hecke-Maaß cusp form of square-free level N, character χ and Laplacian eigenvalue λ≥1/4. It is shown that ‖f‖∞≪λN−1/37, from which the hybrid bound ‖f‖∞≪λ1/4(Nλ)−δ (for some δ>0) is derived. The first bound holds also for f=yk/2F where F is a holomorphic cusp form of weight k with the implied constant now depending on k.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a8778c6c1d0e39bb1c404b50cdbaaa06ce2efc19
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
In Mathematical Physics
Citations in the corpus
- On the sup-norm of Maass cusp forms of large level (2010, background): “For several reasons, see [1, 2, 5], the “trivial” bound is ‖f‖∞ λ, N , while the most optimistic bound would be ‖f‖∞ λ, N−1/2+ .”