Absolute norms of p-primary units

TL;DR

This paper establishes new bounds on the absolute norms of p-primary units in number fields, extending classical results to a local setting and for all primes p.

Contribution

It provides a local analogue of Martinet's theorem and generalizes results to p-primary units for all primes p.

Findings

Proves a local analogue of Martinet's theorem for discriminant ideals.

Establishes bounds on absolute norms of p-primary units for all primes p.

Extends classical global results to local settings in number theory.

Abstract

We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about 2-primary units. We also prove a similar statement about the absolute norms of p-primary units, for all primes p.