Number Theory Seminar

Speaker: Radu Toma (Bonn)

Title: On the size of automorphic forms of large level

Abstract: We investigate the sup-norm problem in the level aspect, which asks for strong bounds on the largest value of automorphic forms as their level grows to infinity. For prime levels, we obtain the first such bounds for Hecke-Maaß newforms in higher rank. Along the way we study the symmetries of the locally symmetric spaces corresponding to the Hecke congruence subgroups in PGL(n), generalising Atkin-Lehner operators. This allows for developing a new reduction theory with level structure. These tools are important for solving the matrix counting problem at the core of the method, where we use an approach based on the geometry of numbers.

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