An extension of the Fukaya-Kato method

TL;DR

This paper refines the Fukaya-Kato method to better understand the role of p-adic L-functions in relating modular symbols and cyclotomic units, advancing the theoretical framework in number theory.

Contribution

It introduces an extension of the Fukaya-Kato method that provides deeper insights into the influence of p-adic L-functions on modular symbols and cyclotomic units.

Findings

Refined the Fukaya-Kato method to incorporate p-adic L-functions more explicitly.

Provided new theoretical insights into the relationship between modular symbols and cyclotomic units.

Enhanced understanding of the role of zeros of p-adic L-functions in number theory.

Abstract

In a groundbreaking paper, T. Fukaya and K. Kato proved a slight weakening of a conjecture of the author's relating modular symbols and cup products of cyclotomic units under an assumption that a Kubota-Leopoldt p-adic L-function has no multiple zeros. This article describes a refinement of their method that sheds light on the role of the p-adic L-function.