Higher Chow cycles on Jacobian of Fermat curves and Hypergeometric functions

Subham Sarkar

paper

Higher Chow cycles on Jacobian of Fermat curves and Hypergeometric functions

arXiv:1703.10370

Abstract

In this paper we construct certain higher Chow cycles in the $K_{1}$ of the Jacobian of Fermat curves, generalising a construction of Collino. We further compute the regulator of these elements in terms of special values of hypergeometric functions. Otsubo has computed the regulator of certain elements of $K_{0}$ and $K_{2}$ of Fermat varieties and this paper is along the same lines.