Mathematical Science Seminar: On Drinfeld cusp forms and Atkin-Lehner operator



Dr Maria Valentino
King's College London, UK


We shall begin with an introduction to Drinfeld modular forms and Teitelbaum's interpretation of Drinfeld cusp forms (DCF for short) as harmonic cocycles. We shall make use of this interpretation to study the Atkin-Lehner $U$-operator acting on DCF. In particular, we shall address the problem of the diagonalizability of $U$ acting on DCF for the arithmetic subgroups $\Gamma_1(T)$ and $\Gamma(T)$.