A Spiegelungssatz for function field $L$-series

TL;DR

This paper establishes a reflection principle for non-archimedean $L$-series in positive characteristic and investigates properties of generalized class modules, advancing understanding in function field arithmetic.

Contribution

It introduces a reflection principle for specific $L$-series and analyzes the pseudo-cyclicity and pseudo-nullity of generalized class modules in positive characteristic.

Findings

Proved a reflection principle for certain non-archimedean $L$-series.

Established pseudo-cyclicity of generalized class modules.

Demonstrated pseudo-nullity of these modules.

Abstract

We prove a kind of reflection principle for certain non-archimedean $L$-series in positive characteristic. We also prove the pseudo-cyclicity and pseudo-nullity of certain several variable generalizations of the class modules introduced by L. Taelman in 2010.