Special values of L-functions and false Tate curve extensions II

TL;DR

This paper combines p-adic Rankin-Selberg methods with Hecke module freeness results to establish congruences between special L-values, supporting deep conjectures in non-commutative Iwasawa theory.

Contribution

It introduces a novel approach to relate p-adic L-values and Hecke modules, advancing understanding of false Tate curve extensions and related conjectures.

Findings

Established new congruences between special L-values

Connected p-adic Rankin-Selberg products with Hecke module structures

Supported conjectural frameworks in non-commutative Iwasawa theory

Abstract

In this paper we show how one can combine the p-adic Rankin-Selberg product construction of Hida with freeness results of Hecke modules of Wiles to establish interesting congruences between special values of L-functions. These congruences is a part of some deep conjectural congruences that follow from the work of Kato on the non-commutative Iwasawa theory of the false Tate curve extension.