Student Number Theory Seminar 2019-20

2/3/20: Paul Garrett -- Self-adjoint operators and zeta functions

Abstract: One hundred years ago, when the theory of self-adjoint operators wasjust being developed, Hilbert and Polya independently speculated on the possibility of using self-adjoint operators (the fact that all eigenvalues are real) to prove the Riemann Hypothesis. In 1977, a flawed numerical computation of eigenvalues of the invariant Laplace-Beltrami operator on the modular curve seemed to indicate that zeros of zeta appeared as spectral parameters.


Back to main page