Hasse-weil bound

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August undefined, 2024

WebMar 26, 2016 · The Hasse–Weil bound on reducible curves was obtained in to extend Wolfmann’s minimum distance bound on cyclic codes to more general class of cyclic … 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 ...

ag.algebraic geometry - Bounds for the number of points on …

WebNov 1, 2024 · The Hasse–Weil bound is a powerful tool for proving such conjectures asymptotically, i.e., when the finite field is sufficiently large. Usually, when applying the … http://aiezzi.it/documents/art4.pdf bouchon silver plate espresso spoons

Hasse–Weil bound for additive cyclic codes SpringerLink

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 and its variations have many applications in the study of polynomial equations over nite elds. In this paper, we use the above observations to prove the following result. Theorem 1.1. Assume that two rational functions f(X);g(X) 2F q(X) nF q with degf= dand degg= satisfy the following conditions. (i) f(F q) ˆg(Fy). (ii ... 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 etc. In general, the bound is tight and cannot be improved. However, for some special families of curves the bound could be improved substantially. In this paper, we focus on … bouchon sirius

Some Sextics of Genera Five and Seven Attaining the Serre Bound …

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. WebJul 4, 2024 · The Hasse-Weil bound requires smooth curves, and hyperelliptic curves are not smooth if the degree is greater than three, having only one singular point. We have explicit example violating the Hasse-Weil bound with only one singular point. abx claims "A projective hyperelliptic curve is smooth by definition." bouchon sm562WebJun 22, 2024 · We use the Aubry-Perret bound for singular curves, a generalization of the Hasse-Weil bound, to prove the following curious result about rational functions over finite fields: Let... Global Survey In just 3 minutes help us understand how you see arXiv . bouchon silicone 10mm

"WebPollard’s p 1 algorithm is explained, as well as the Hasse-Weil Bound, after which follows a discussion of how Lenstra’s Algorithm improves upon Pollard’s. Then Lenstra’s … " - Hasse-weil bound

Hasse-weil bound

Wiman’s and Edge’s sextics attaining Serre’s bound

WebDec 30, 2024 · Among another family, we find new curves of genus 7 attaining the Hasse–Weil–Serre bound over $\mathbb {F}_{p^3}$ for some primes p. We determine the precise condition on the finite field over which the sextics attain the Hasse–Weil–Serre bound. Keywords. Algebro-geometric codes; Rational points; Serre bound WebWe hypothesize that methods for hyperelliptic curves can be generalized to the case of superelliptic curves with similar runtimes. Approach: Under a few constraints, the Hasse-Weil bound ensures that the number of points modulo p uniquely determines the actual number of points (#C(F_p)) on a curve C over the finite field F_p.

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WebLove Bound is a 1932 American Pre-Code mystery film directed by Robert F. Hill and starring Jack Mulhall, Natalie Moorhead, Clara Kimball Young. It is a second feature … WebIn mathematics, the Weil conjectures were highly influential proposals by André Weil ( 1949 ). They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory . The conjectures concern the generating functions (known as local zeta functions ...

WebOct 30, 2013 · 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. … WebMay 17, 2024 · which was proved by Hasse for elliptic curves in 1933, and extended to all algebraic curves by Weil in 1941. The algebraic curve is said to be maximal if it attains this bound. Here p is a prime and q is its power.

WebJan 1, 2024 · By comparing (2) and (5) with the Hasse-Weil bound (1) we obtain d λ ≤ λ + 2 g (C k) λ, which leads to λ ≤ 4 g (C k) 2 (d − 1) 2 in the case d > 1. This observation is a crucial ingredient in the verification process: If p is picked such that its norm λ is sufficiently greater than 4 g (C k) 2 (d − 1) 2, we Webgoal is to understand the proof of Deligne’s Weil II, as well as the theory of trace functions, without learning French. 2 Hasse bound for elliptic curves 2.1 Manin’s elementary proof …

WebJan 4, 2024 · This bound improved the Weil bound for high degree polynomials with small indices as well as polynomials with large indices that are generated by cyclotomic mapping of small indices. (3) Recently, there is an improvement on the Hasse-Weil bound in the characteristic two case by Cramer and Xing . They used the algebraic geometry and the ...

WebThe corresponding Hasse-Weil bound was a major breakthrough in his-tory of mathematics. It has found many applications in mathematics, coding theory and theoretical computer science. In general, the Hasse-Weil bound is tight and can-not be improved. However, the Hasse-Weil bound is no longer tight when it is applied bouchons kelowna bcWebThe 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. The proof was provided by … bouchon slow flowWebMar 17, 2024 · The Hasse–Weil bound is a deep result in mathematics and has found wide applications in mathematics, theoretical computer science, information theory etc. In … bouchon skimmer piscineWebFeb 16, 2024 · To each such curve C one can associate a genus g; for instance, elliptic curves have genus 1. We can also count the cardinality C ( F q) of the set C ( F q) of F … bouchons lyonnais lyon 2WebMar 7, 2016 · 3. I know that the well-known Weil bound for character sums is given by. ∑ x ∈ F q χ ( f ( x)) ≤ ( d − 1) q. where F q is a finite field of size q, χ is a multiplicative character of order m, f ∈ F q [ x] is a polynomial of positive degree that is not an m th power of a polynomial, and d is the number of distinct roots of f in F ... bouchons lyonnais fourviereWebthe Hasse-Weil Upper Bound Arnaldo Garcia Abstract. Curves over ﬁnite ﬁelds (whose cardinality is a square) attaining the Hasse-Weil upper bound for the number of rational … bouchons maleWebJun 22, 2024 · Title:An Application of the Hasse-Weil Bound to Rational Functions over Finite Fields Authors:Xiang-dong Hou, Annamaria Iezzi Download PDF Abstract:We use … bouchon smartfit