Number Theory Seminar

Spectral reciprocity links seemingly disparate automorphic spectra and provides a powerful framework for subconvexity and higher-moment problems of automorphic L-functions. In this talk, we present new perspectives that lead to broader reciprocity relations and concrete arithmetic applications. The approach blends regularization with Fourier analysis and leverages underlying automorphic, algebraic, and geometric structures, offering a complementary viewpoint to classical purely analytic methods.