Webinaire EFI

The spectral zeta function associated with the roots of an E-function

by Mr Peter Jossen (Zurich )


I will present a few observations about the distribution of roots of E-functions in the complex plane. The "spectral zeta function" of an E-function
f(z) is then defined as the sum ranging over all roots of f raised to a complex powers. It converges absolutely for Re(s) >1. I will show that this
zeta function admits an analytic continuation to the whole complex s-plane, and calculate some special values