R\'egulateurs modulaires explicites via la m\'ethode de Rogers-Zudilin

TL;DR

This paper computes regulators of certain algebraic elements using special values of L-functions of modular forms, applying the Rogers-Zudilin method to connect these concepts.

Contribution

It introduces a novel application of the Rogers-Zudilin method to explicitly compute regulators in algebraic K-theory related to modular forms.

Findings

Explicit formulas for regulators in terms of L-values

Connection established between regulators and special L-values

Method demonstrated on specific algebraic elements

Abstract

We compute the regulator of Beilinson-Deninger-Scholl elements in terms of special values of L-functions of modular forms, using the Rogers-Zudilin method.