International Seminar on Automorphic Forms

Katy Woo (Stanford University): Sums of Hecke eigenvalues along polynomials and arithmetic applications

We study sums of absolute values of Hecke eigenvalues of GL(2) representations that are tempered at all finite places. We show that these sums exhibit logarithmic savings over the trivial bound if and only if the representation is cuspidal. Further, we connect the problem of studying the sums of Hecke eigenvalues along polynomial values to the base change problem for GL(2). Finally, we will describe some arithmetic applications of bounds on these sums for counting rational points on del Pezzo surfaces.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits)