Hasse’s bound for elliptic curves over finite fields
Let be an elliptic curve defined over a finite field with elements ( is a prime). The following theorem gives a bound of the size of , , i.e. the number points of defined over . This was first conjectured by Emil Artin (in his thesis!) and proved by Helmut Hasse in the 1930’s.
Theorem 1 (Hasse).
Remark: Let as in the definition of the L-series of an ellitpic curve. Then Hasse’s bound reads:
This fact is key for the convergence of the L-series of .
|Title||Hasse’s bound for elliptic curves over finite fields|
|Date of creation||2013-03-22 13:55:41|
|Last modified on||2013-03-22 13:55:41|
|Last modified by||alozano (2414)|