The $\chi$-part of the analytic class number formula, for global function fields

TL;DR

This paper proves a complex Gras conjecture for Stark units in global function fields and derives a refined analytic class number formula, advancing understanding of class number relations in this setting.

Contribution

It establishes a complex Gras conjecture for Stark units and refines the analytic class number formula in the context of global function fields.

Findings

Proves a complex Gras conjecture for Stark units

Derives a refined analytic class number formula

Advances the understanding of class number relations in function fields

Abstract

Let F/k be a finite abelian extension of global function fields, totally split at a distinguished place \infty. We prove that a complex Gras conjecture holds for a suitable group of Stark units, and we derive a refined analytic class number formula.