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The Hasse Norm Principle in Global Function Fields

Number Theory 2024-01-29 v1

Abstract

Let LL be a finite extension of Fq(t)\mathbb{F}_q(t). We calculate the proportion of polynomials of degree dd in Fq[t]\mathbb{F}_q[t] that are everywhere locally norms from L/Fq(t)L/\mathbb{F}_q(t) which fail to be global norms from L/Fq(t)L/\mathbb{F}_q(t).

Keywords

Cite

@article{arxiv.2003.01451,
  title  = {The Hasse Norm Principle in Global Function Fields},
  author = {Adelina Mânzăţeanu and Rachel Newton and Ekin Ozman and Nicole Sutherland and Rabia Gülşah Uysal},
  journal= {arXiv preprint arXiv:2003.01451},
  year   = {2024}
}