Regulators of K_2 of Hypergeometric Fibrations

TL;DR

This paper explores the Beilinson regulator on K_2 of hypergeometric fibrations, expressing regulators through hypergeometric functions and discussing implications for special values of L-functions.

Contribution

It provides a novel description of regulators using hypergeometric functions for hypergeometric fibrations, advancing understanding of Beilinson's conjecture.

Findings

Regulators are expressed via hypergeometric functions 3F2 and 4F3.

Connections made between regulators and special values of L-functions.

Insights into Beilinson's conjecture for these fibrations.

Abstract

We discuss Beilinson's regulator on K_2 of certain fibrations of algebraic varieties which we call the hypergeomtric fibrations. The main result is to describe regulators via the hypergeometric functions 3F2 or 4F3. We also discuss the Beilinson conjecture on the special values of L-functions.