Work

Bounds on Fourier coefficients and global sup‐norms for Siegel cusp forms of degree 2

Year: 2025

Type: article

Abstract: Let be an ‐normalized Siegel cusp form for of weight that is a Hecke eigenform and not a Saito–Kurokawa lift. Assuming the generalized Riemann hypothesis, we prove that its Fourier coefficients satisfy the bound where denotes the gcd of the entries of , and that its global sup‐norm satisfies the bound . The former result depends on new bounds that we establish for the relevant local integrals appearing in the refined global Gan–Gross–Prasad conjecture (which is now a theorem due to Furusawa and Morimoto) for Bessel periods.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70119

Authors: Félicien Comtat, Jolanta Marzec‐Ballesteros, Abhishek Saha

Institutions: University of Bonn, Adam Mickiewicz University in Poznań, Queen Mary University of London

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Leverhulme Trust, Engineering and Physical Sciences Research Council