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Class Number One Problem for Imaginary Function Fields: The Cyclic Prime Power Case

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
84
Issue
1
Identifiers
DOI: 10.1006/jnth.2000.2535

Abstract

Abstract In this paper, we determine all finite separable imaginary extensions K/ F q ( x) whose maximal order is a principal ideal domain in case K/ F q ( x) is a non zero genus cyclic extension of prime power degree. There exist exactly 42 such extensions, among which 7 are non isomorphic over F q .

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