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On elliptic function fields with the class number p+1 over finite prime fields of characteristic p≠2,3


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Title: On elliptic function fields with the class number p+1 over finite prime fields of characteristic p≠2,3
Authors: Washio, Tadashi
Authors (alternative): 鷲尾, 忠司
Issue Date: 28-Feb-1973
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.24, p.7-11; 1973
Abstract: Let k be a finite prime field of characteristic p which differs from 2 and 3. Let K be an elliptic function field over k and denote by h the class number of K, It is shown that, in the case where K is defined by the equation y2=x3-a, (a≠0, a∈k), a necessary and sufficient condition of the equality h=p+1 is the congruence p≡2 mod. 3, and that, in the case where K is defined by the equation y2=x3-ax, (a≠0, a∈k), a necessary and sufficient condition of the equality h=p+1 is the congruence p≡3 mod. 4.
URI: http://hdl.handle.net/10069/32974
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 24

Citable URI : http://hdl.handle.net/10069/32974

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