Ryojun Ito
Published 2016-05-04Version 1
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 conjecture originally due to Bloch.
$L$-function of CM elliptic curves and generalized hypergeometric functions
The density and distribution of CM elliptic curves over $\mathbb{Q}$
On the Constants of the Lang-Trotter Conjecture for CM Elliptic Curves
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