### Integrals of Z-functions

Heilbronn Number Theory Seminar

8th March 2023, 4:00 pm – 5:00 pm

Fry Building, 2.04

The Z-function associated to an L-function is a rotated real-valued function defined so that |Z(t)| = |L(1/2 + it)|, so that critical zeros of L(s) are real zeros, and presumably sign changes, of Z(t). For the zeta function, the integral of Z(t) is well-understood. I'll discuss the integral for (mostly) Dirichlet L-functions, and some phenomena in the spacings of zeros of zeta and L-functions discovered along the way.

This is joint work with Zhenchao Ge and Micah Milinovich.

*Biography:*

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