The Hasse Norm Principle in Global Function Fields

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Copy For Citation

Uysal R. G., Özman E., Newton R., Manzateanu A., Sutherland N.

in: Women in Numbers Europe 3, Alina Carmen Cojocaru,Sorina Ionica,Elisa Lorenzo Garcia, Editor, Springer Nature, Zug, pp.275-290, 2022

• Publication Type: Book Chapter / Chapter Research Book
• Publication Date: 2022
• Publisher: Springer Nature
• City: Zug
• Page Numbers: pp.275-290
• Editors: Alina Carmen Cojocaru,Sorina Ionica,Elisa Lorenzo Garcia, Editor
• Middle East Technical University Affiliated: Yes

Abstract

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