Results 31 to 40 of about 549 (46)

Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average

, 2007
We prove that the set of Farey fractions of order $T$, that is, the set $\{\alpha/\beta \in \Q : \gcd(\alpha, \beta) = 1, 1 \le \alpha, \beta \le T\}$, is uniformly distributed in residue classes modulo a prime $p$ provided $T \ge p^{1/2 +\eps}$ for any ...
Cojocaru, A. C., Shparlinski, I. E.
core   +1 more source

The dihedral hidden subgroup problem

Journal of Mathematical Cryptology
The hidden subgroup problem (HSP) is a cornerstone problem in quantum computing, which captures many problems of interest and provides a standard framework algorithm for their study based on Fourier sampling, one class of techniques known to provide ...
Chen Imin, Sun David
doaj   +1 more source

Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves [PDF]

, 2007
Let $\E/\Q$ be a fixed elliptic curve over $\Q$ which does not have complex multiplication. Assuming the Generalized Riemann Hypothesis, A. C. Cojocaru and W.
Shparlinski, Igor E.
core   +3 more sources

On elliptic curves with a closed component passing through a hexagon

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In general, there exists an ellipse passing through the vertices of a convex pentagon, but any ellipse passing through the vertices of a convex hexagon does not have to exist.
Kureš Miroslav
doaj   +1 more source

Modular Invariant of Quantum Tori II: The Golden Mean [PDF]

, 2012
In our first article in this series ("Modular Invariant of Quantum Tori I: Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of quantum tori was defined.
Bernard, C. Castaño, Gendron, T. M.
core  

Balanced factorisations

, 2016
Any rational number can be factored into a product of several rationals whose sum vanishes. This simple but nontrivial fact was suggested as a problem on a maths olympiad for high-school students.
Klyachko, Anton A., Vassilyev, Anton N.
core   +1 more source

On the first fall degree of summation polynomials

Journal of Mathematical Cryptology, 2019
We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.
Kousidis Stavros, Wiemers Andreas
doaj   +1 more source

Application of Mordell–Weil lattices with large kissing numbers to acceleration of multiscalar multiplication on elliptic curves

Journal of Mathematical Cryptology
This article aims to speed up (the precomputation stage of) multiscalar multiplication (MSM) on ordinary elliptic curves of j-invariant 0 with respect to specific “independent” (also known as “basis”) points.
Koshelev Dmitrii
doaj   +1 more source

A new family of elliptic curves with positive ranks arising from the Heron triangles [PDF]

, 2010
The aim of this paper is to introduce a new family of elliptic curves with positive ranks. These elliptic curves have been constructed with certain rational numbers, namely a, b, and c as sides of Heron triangles having rational areas $k$.
Izadi, F. A., Khoshnam, Foad, Nabardi, K.   +2 more
core  

Noncommutative geometry of rational elliptic curves

, 2017
We study an interplay between operator algebras and geometry of rational elliptic curves. Namely, let $\mathcal{O}_B$ be the Cuntz-Krieger algebra given by square matrix $B=(b-1, ~1, ~b-2, ~1)$, where $b$ is an integer greater or equal to two.
Nikolaev, Igor
core   +1 more source