Abstract:
In this talk, I will discuss the calculation of the regulators of Fermat curves via the Rankin-Selberg method. One of the key points of the study is the use of a distinguished uniformization of Fermat curves by the Poincare upper half plane. By using this uniformization, we study a variant of Ross elements and distinguished Eisenstein series attached to them. Then the calculation of the regulator is reduced to that of the Rankin-Selberg integrals. As a result, we prove Beilinson's conjecture for the quartic Fermat curve. This is a joint work with Kenji Sakugawa.