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On Class Numbers of Hyperelliptic Function Fields

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Title: On Class Numbers of Hyperelliptic Function Fields
Other Titles: 超楕円関数体の類数について
Authors: 鷲尾, 忠司
Authors (alternative): Washio, Tadashi
Issue Date: 28-Feb-1978
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.29, p.1-3; 1978
Abstract: Let F=GF(p) be a finite prime field of characteristic p≠2. Let K=F(x,y) be a hyperelliptic function field over F defined by an equation y2=xn+a (a≠O, a∈F), where n denotes an odd number such that n>1 and p∤n. Let h be the class number of K and g the genus of K. Then, we have proved that h=p+1 if n=3 and p≡2 mod 3. (〔4〕, Theorem 1 (i)). This particular fact can be generally expressed as follows; Given n, there exists an integer c such that h=pg+ 1 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/10069/32718
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 29

Citable URI : http://hdl.handle.net/10069/32718

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