The Hasse–Weil bound reduces to the usual Hasse bound when applied to elliptic curves, which have genus g=1. The Hasse–Weil bound is a consequence of the Weil conjectures, originally proposed by André Weil in 1949 and proved by André Weil in the case of curves. See also. Sato–Tate conjecture; See more 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 … See more A generalization of the Hasse bound to higher genus algebraic curves is the Hasse–Weil bound. This provides a bound on the number of points on a curve over a finite field. If the … See more • Sato–Tate conjecture • Schoof's algorithm • Weil's bound See more WebOct 30, 2013 · Abstract: A curve attaining the Hasse-Weil bound is called a maximal curve. Usually, classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical error-correcting codes via Euclidean or Hermitian self-orthogonality do not always possess …
Curves over Finite Fields Attaining the Hasse-Weil …
WebApr 7, 2024 · 1 The Hasse-Weil bound implies that for any 2-variable polynomial P ( x, y), there exists approximately p solutions in F p of P ( x, y) ≡ a ( mod p) for sufficiently large p, and any integer a. The Chevalley Theorem gives a sufficient condition for a homogeneous n -variable polynomial to have nontrivial roots in F p. WebThe Hasse–Weil bound reduces to the usual Hasse bound when applied to elliptic curves, which have genus g=1. The Hasse–Weil bound is a consequence of the Weil conjectures , originally proposed by André Weil in 1949 and proved by André Weil in the case of curves. chewy gluten free sugar cookies
Hasse
WebMay 7, 2015 · Abstract: The Hasse-Weil bound is a deep result in mathematics and has found wide applications in mathematics, theoretical computer science, information theory … WebIt’s also referred to as the Hasse bound, because as a result the value is bounded both above and below." but I don't completely understand this result. Proof: Consider the Frobenius endomorphism on E in F q where p … WebMost references simply state that the quadratic character bound, and the general character sum bound are special cases of counting points on varieties and the Riemann hypothesis. But how are the two results related in the general case, where $\chi$ no longer takes only 1/-1 values? Is there a simple correspondence like in the quadratic case ... chewy good and fun treats