Central values of zeta functions of non-Galois cubic fields

TL;DR

This paper investigates the properties of Dedekind zeta functions associated with non-Galois cubic fields, revealing that many have negative values at the central point, which is significant for number theory.

Contribution

It demonstrates that infinitely many non-Galois cubic fields have Dedekind zeta functions with negative central values, a novel insight into their distribution.

Findings

Infinitely many non-Galois cubic fields have negative central zeta values.

Provides evidence for the variability of zeta function signs in cubic fields.

Contributes to understanding the analytic behavior of zeta functions in algebraic number theory.

Abstract

The Dedekind zeta functions of infinitely many non-Galois cubic fields have negative central values.