The Beilinson Conjectures for CM Elliptic Curves via Hypergeometric Functions

Ryojun Ito

paper

The Beilinson Conjectures for CM Elliptic Curves via Hypergeometric Functions

arXiv:1605.01145

Abstract

We consider certain CM elliptic curves which are related to Fermat curves, and express the values of $L$ -functions at $s = 2$ in terms of special values of generalized hypergeometric functions. We compare them and a similar result of Rogers-Zudilin with Otsubo's regulator formulas, and give a new proof of the Beilinson conjectures originally due to Bloch.

14 pages