Date: Wednesday, February 20, 2013
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: Zagier's Magic Formulas for Real Quadratic Fields
Abstract: If $K$ is an imaginary quadratic field, the zeta function $\zeta_K(s,A)$ of an ideal class $A$ of $\mathcal{O}_K$ is essentially a real analytic Eisenstein series. Instead let $K$ be real quadratic; this is no longer the case. However, an elementary trick due to Hecke expresses $\zeta_K(s,A)$ as the integral of real analytic Eisenstein series over a geodesic in the upper half plane. We will discuss (and sketch the proof of) some mind-blowing formulas of Meyer and Zagier relating the constant term of $\zeta_K(s,A)$ at $s=1$ to the periods of continued fractions. Connections will be drawn to the Stark conjectures and Hilbert's Twelfth Problem.
Speaker: Gene Kopp
Institution: UM
Event Organizer:
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