Reconstructing global fields from Dirichlet L-series

TL;DR

This paper establishes a criterion for identifying when two global fields are isomorphic based on the isomorphism of their Dirichlet character groups that preserve L-series, linking field structure to analytic properties.

Contribution

It proves that global fields are uniquely determined by the structure of their Dirichlet character groups and the preservation of L-series, providing a new characterization of field isomorphism.

Findings

Global fields are isomorphic iff their Dirichlet character groups are isomorphic with L-series preserved.

The result connects algebraic field properties with analytic L-series data.

Provides a new criterion for field isomorphism based on character groups and L-series.

Abstract

We prove that two global fields are isomorphic if and only if there is an isomorphism of groups of Dirichlet characters that preserves L-series.