Hasse's theorem on elliptic curves

Hasse's theorem on elliptic curves, also referred to as the Hasse bound, provides an estimate of the number of points on an elliptic curve over a finite field, bounding the value both above and below. If N is the number of points on the elliptic curve E over a finite field with q elements, then Helmut Hasse's result states that The reason is that N differs from q + 1, the number of points of the projective line over the same field, by an 'error term' that is the sum of two complex numbers, each of absolute value √q.

Hasse's theorem on elliptic curves

Hasse's theorem on elliptic curves, also referred to as the Hasse bound, provides an estimate of the number of points on an elliptic curve over a finite field, bounding the value both above and below. If N is the number of points on the elliptic curve E over a finite field with q elements, then Helmut Hasse's result states that The reason is that N differs from q + 1, the number of points of the projective line over the same field, by an 'error term' that is the sum of two complex numbers, each of absolute value √q.