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

Félicien Comtat, Jolanta Marzec-Ballesteros, Abhishek Saha

Let $F$ be an $L^2$-normalized Siegel cusp form for ${\mathrm{Sp}}_4(\mathbb{Z})$ of weight $k$ that is a Hecke eigenform and not a Saito--Kurokawa lift. Assuming the Generalized Rie…