Alladi Ramakrishnan Hall

Uniform sup-norm bounds for Siegel cusp forms

Antareep Mandal

IIT Madras

This talk is about obtaining uniform sup-norm bounds of Siegel cusp forms on average over an orthonormal basis. First, we relate Siegel cusp forms to the bottom of the spectrum of the respective weighted Siegel Maass Laplacian. Then we construct and analyze the corresponding heat kernel to arrive at the conjectured optimal bounds for both cocompact and cofinite arithmetic subgroups of the symplectic group. Further, we show that these bounds are uniform over a tower of arithmetic subgroups of finite index.