منابع مشابه
A mean value formula for elliptic curves
It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate.
متن کاملOn Silverman's conjecture for a family of elliptic curves
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...
متن کاملA problem of Linnik for elliptic curves and mean-value estimates for automorphic representations
When Linnik introduced the classical large-sieve in 1941 [Lin], he was motivated by the following problem: given a non-trivial primitive character χ modulo q, how large (compared to q) can be the first n such that χ(n) = 1? From the Riemann Hypothesis one can deduce (see [Mon] chapter 13 for instance) n (log q) 2 and the (weaker) conjecture n q ε for all ε > 0 is known as Vinogradov's conjectur...
متن کاملMean value formulas for twisted Edwards curves
R. Feng, and H. Wu recently established a certain mean-value formula for the x-coordinates of the n-division points on an elliptic curve given in Weierstrass form (A mean value formula for elliptic curves, 2010, available at http://eprint.iacr.org/2009/586.pdf ). We prove a similar result for both the x and y-coordinates on a twisted Edwards elliptic curve.
متن کاملGenus Formula for Modular Curves of D-elliptic Sheaves
We prove a genus formula for modular curves of D-elliptic sheaves. We use this formula to show that the reductions of modular curves of D-elliptic sheaves attain the Drinfeld-Vladut bound as the degree of the discriminant of D tends to infinity.
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ژورنال
عنوان ژورنال: Journal of Numbers
سال: 2014
ISSN: 2356-7511,2314-842X
DOI: 10.1155/2014/298632