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Hasse's theorem on elliptic curves - Wikipedia

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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 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 . This result had originally been conjectured by Emil Artin in his thesis.[1] It was proven by Hasse in 1933, with the proof published in a series of papers in 1936.[2] Hasse's theorem is equivalent to the determination of the absolute value of the roots of the local zeta-function of E. In this form it can be seen to be the analogue of the Riemann hypothesis for the function field associated with the elliptic curve. A generalization of the Hasse bound to higher genus algebraic cur

Hasse's theorem on elliptic curves - Wikipedia Jump to content From Wikipedia, the free encyclopedia Estimates the number of points on an elliptic curve over a finite field 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 Hasse's result states that | N − ( q + 1 ) | ≤ 2 q . {\displaystyle |N-(q+1)|\leq 2{\sqrt {q}}.} The reason is that N differs fr

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