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On elliptic function fields with the class number p+1 over finite prime fields of characteristic p≠2,3
| Content Provider | Semantic Scholar |
|---|---|
| Author | Washio, Tadashi |
| Copyright Year | 1972 |
| 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. |
| Starting Page | 7 |
| Ending Page | 11 |
| Page Count | 5 |
| File Format | PDF HTM / HTML |
| Volume Number | 24 |
| Alternate Webpage(s) | http://naosite.lb.nagasaki-u.ac.jp/dspace/bitstream/10069/32974/1/kyoikuS24_007.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
