Math and Stats Colloquium: The Goss Zeta Function

Friday, Nov. 15, 2024, 4–5 p.m.

James Upton - UC Santa Cruz

Title: The Goss zeta function

Abstract: A central theme in number theory is the analogy between rational numbers and rational functions over a field F. When F is finite, Goss constructed a zeta function which, under this analogy, plays the analogue of the Riemann zeta function. This talk describes the history of the Goss zeta function and its many interesting parallels to the Riemann zeta function. We describe some classical results concerning its special values, as well as what is known about the distribution of its zeros. We also describe some recent work generalizing these results to arbitrary function fields over F. This is joint work with Joe Kramer-Miller.

Mathematics and Statistics Colloquium Series