Cécile Armana

Sturm bounds for Drinfeld-type automorphic forms over function fields

Sturm bounds say how many successive Fourier coefficients are sufficient to determine a modular form of a given weight and level. For classical modular forms, they also provide explicit bounds for the number of Hecke operators generating the Hecke algebra. I will review the situation over the rational function field F_q(t) for "Drinfeld-type" automorphic forms and their Hecke algebra. Sturm bounds are obtained using refinements of a fundamental domain for a Bruhat-Tits tree under the action of a congruence subgroup. This is joint work with Fu-Tsun Wei (National Tsing Hua University, Taiwan).