The Beilinson Conjectures for CM Elliptic Curves via Hypergeometric Functions

Ryojun Ito

The Beilinson Conjectures for CM Elliptic Curves via Hypergeometric Functions

Number Theory 2016-06-30 v2

Authors: Ryojun Ito

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.

Keywords

elliptic curves

Cite

@article{arxiv.1605.01145,
  title  = {The Beilinson Conjectures for CM Elliptic Curves via Hypergeometric Functions},
  author = {Ryojun Ito},
  journal= {arXiv preprint arXiv:1605.01145},
  year   = {2016}
}

Comments

14 pages

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