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September 2019 On the $p$-divisibility of class numbers of cyclotomic function fields
Daisuke Shiomi
Funct. Approx. Comment. Math. 61(1): 85-94 (September 2019). DOI: 10.7169/facm/1757

Abstract

Let $\mathbb{F}_q$ be the finite field with $q=p^r$ elements, where $p$ is a prime. For a monic $m \in \mathbb{F}_q[T]$, let $h_m$ be the class number of the $m$th cyclotomic function field. The goal of this paper is to determine the $p$-divisibility of $h_m$ when $q = p$ $(r \ge 2)$ and $\deg m=2$.

Citation

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Daisuke Shiomi. "On the $p$-divisibility of class numbers of cyclotomic function fields." Funct. Approx. Comment. Math. 61 (1) 85 - 94, September 2019. https://doi.org/10.7169/facm/1757

Information

Published: September 2019
First available in Project Euclid: 26 October 2018

zbMATH: 07126911
MathSciNet: MR4012363
Digital Object Identifier: 10.7169/facm/1757

Subjects:
Primary: 11R29, 11R60

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.61 • No. 1 • September 2019
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