Generalization of the "Stark unit" for abelian L-functions with multiple zeros

TL;DR

This paper establishes an equivalence between the Stark conjecture for abelian L-functions with multiple zeros and the existence of a special algebraic element related to units in number fields, advancing understanding of L-function zeros.

Contribution

It generalizes the Stark conjecture to cases with multiple zeros, linking it to the existence of specific elements in the exterior power of units in abelian extensions.

Findings

Equivalence between Stark conjecture and special elements in unit modules

Extension of Stark conjecture to multiple zero cases

Provides a new algebraic framework for understanding L-function zeros

Abstract

For an abelian extension of number fields we show that the Stark conjecture for all Artin L-functions with zero of order r is equivalent to existence of a special element in the rational span of the r-th exterior power of the Galois module of units of the bigger field.