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On Class Numbers of Hyperelliptic Function Fields-2

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Title: On Class Numbers of Hyperelliptic Function Fields-2
Authors: Washio, Tadashi
Issue Date: 29-Feb-1980
Publisher: 長崎大学教育学部
Citation: 長崎大学教育学部自然科学研究報告. vol.31, p.1-4; 1980
Abstract: Let F=GF (p) be a finite prime field of characteristic p≠2. Let K=F(x, y) be an algebraic functicon field over F defined by an equation y2=xn - a (a≠0, a∈F), where n means an odd number so that n > 1 and p∤n. Let h be the class number of K and g the genus of K..Then, it is obvious that h=p +1 if n=3 and p≡2 mod 3. This particular fact can be generally expressed as follows; Given n, there exists an integer c such that h= (p +1)g whenever p≡c mod n. In this note, it is shown that this generalization is true in the particular case of n=5 and of n=7.
URI: http://hdl.handle.net/10069/32669
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 31

Citable URI : http://hdl.handle.net/10069/32669

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