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

概要

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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.
長崎大学教育学部の論文
1973-02-28