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On Class Numbers of Hyperelliptic Function Fields-3-


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Title: On Class Numbers of Hyperelliptic Function Fields-3-
Authors: Washio, Tadashi
Issue Date: 28-Feb-1981
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, 32: 1-6
Abstract: Let F= GF(P) be a finite prime field of characteristic P≠2. Let K=F(x,y) be an algebraic function field over F defined by an equation y2= x2g+1- ax (a≠0,a∈F),where g means a positive integer. Let us denote by h the class number of K.. Then, it is obvious that h=p+1 if g=1 and p≡3 mod 4. This particular fact can be generally expressed as follows; Given g, there exists an integer c such that h= (p+1)g whenever p≡c mod 4g. In this note, it is shown that this generalization is true in the particular case of g = 2 and of g = 3.
URI: http://hdl.handle.net/10069/32617
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 32

Citable URI : http://hdl.handle.net/10069/32617

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