International Seminar on Automorphic Forms

The theta correspondence between the orthogonal group and the symplectic group  provides a cornerstone for studying Siegel modular forms via orthogonal modular forms. In this work, we make this correspondence completely explicit, with precise level structure for low to moderate even rank and nontrivial discriminant. Guided by computational discoveries, we prove congruences between eigenvalues of classical modular forms and eigenvalues of genuine Siegel modular forms, obtain formulas for the number of neighbors in terms of eigenvalues of classical modular forms, and formulate some conjectures that arise naturally from the data. This is joint work with Dan Fretwell, Colin Ingalls, Adam Logan, Spencer Secord, and John Voight

Eran Assaf (Dartmouth College)

You can join the Zoom meeting at https://tu-darmstadt.zoom.us/j/68048280736

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