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Constructions of elliptic curves endomorphisms
Математические вопросы криптографии. 2014. Vol. 5. No. 2. P. 99-102.
In this article we present an algorithm for constructing an elliptic curve endomorphism for given complex irrationality. This endomorphism can be used for speeding up a group operation on elliptic curve.
Smirnov E., Квант 2020 № 5 С. 15-24
В статье рассказывается о числовых фризах Конвея-Кокстера и обсуждаются их основные свойства. ...
Added: September 19, 2020
Frolenkov D., Математический сборник 2012 Т. 203 № 2 С. 143-160
В работе рассматриваются первые моменты для числа шагов в различных алгоритмах Евклида. Для них, используя улучшенные оценки сумм дробных долей и идеи из элементарного доказательства А.Сельберга асимптотического закона распределения простых чисел, получены асимптотические формулы с новыми остаточными членами ...
Added: November 3, 2014
Poberezhny V. A., / ИТЭФ. Series "Препринты ИТЭФ". 2012. No. 57/12.
In this work we investigate the action of generalized Schlesinger transformation on the isomonodromic families of meromorphic connections on the linear bundles of rank two and degree zero over an elliptic curve. The main interest is the action of the gauge transformation on the moduli space of vector bundles. the central result is the explicit ...
Added: March 31, 2014
Bogomolov F. A., Fu H., European Journal of Mathematics 2016 Vol. 2 No. 3 P. 644-660
Given two elliptic curves, each of which is associated with a projection map that identifies opposite elements with respect to the natural group structure, we investigate how their corresponding projective images of torsion points intersect. ...
Added: August 31, 2016
Nesterenko A., Математические вопросы криптографии 2016 Vol. 7 No. 2 P. 115-120
We propose an algorithm for solving the discrete logarithm problem on the elliptic curve. This algorithm uses additional information on the multiplicative order of the solution and may be realised in parallel. ...
Added: November 16, 2016
Рукавишникова М. Г., Математические заметки 2011 Т. 90 № 3 С. 431-444
We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients. ...
Added: July 20, 2015
Buff X., Goncharuk N. B., / Cornell University. Series math "arxiv.org". 2013. No. 1308.3510.
We investigate the notion of complex rotation number which was introduced by V.I.Arnold in 1978. Let f: R/Z \to R/Z be an orientation preserving circle diffeomorphism and let {\omega} \in C/Z be a parameter with positive imaginary part. Construct a complex torus by glueing the two boundary components of the annulus {z \in C/Z | ...
Added: December 12, 2013
Frolenkov D., Kan I. D., Moscow Journal of Combinatorics and Number Theory 2014 Vol. 4 No. 1 P. 78-117
Zaremba's conjecture (1971) states that every positive integer number can be represented as a denominator (continuant) of a finite continued fraction with all partial quotients being bounded by an absolute constant A. Recently (in 2011) several new theorems concerning this conjecture were proved by Bourgain and Kontorovich. The easiest of them states that the set of ...
Added: November 1, 2014
Рукавишникова М. Г., Чебышевский сборник 2006 Т. 7 № 4 С. 113-121
a ...
Added: July 20, 2015
Brown F., / arxive. Series math "nt". 2013. No. arXiv:1110.6917v2.
Abstract. We study the de Rham fundamental group of the configuration space
E (n) of n + 1 marked points on a complex elliptic curve E, and define multiple
elliptic polylogarithms. These are multivalued functions on E (n) with unipotent
monodromy, and are constructed by a general averaging procedure. We show
that all iterated integrals on E (n) , ...
Added: May 14, 2014
Brown F., Levin A., / Cornell University. Series arXiv "math". 2013. No. 1110.6917 [.
Abstract. We study the de Rham fundamental group of the configuration sp ace of several marked points on a complex elliptic curve, and define multiple elliptic polylogarithms. These are multivalued functions with unipotent monodromy, and are constructed by a general averaging proce dure. We show that all iterated integrals on this configuration space can be ...
Added: October 4, 2013
Netay I. V., Савватеев А. В., / Cornell University. Series math "arxiv.org". 2016.
The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles.
We call them Sharygin triangles.
It turns out that they are parametrized by an open subset of an elliptic curve.
Also we prove that there are infinitely many non-similar integer ...
Added: October 19, 2016
Gutnik L., / Cornell University Library. 2013. No. 1307.1125.
We present here continued fraction for Zeta(3) parametrized by some family of points (F,G) on projective line. This family of points can be obtained if from full projective line would be removed some no more than countable nowhereмножество dense exeptional set of finite points. countable nowhere dense set, which contains the above exeptional set of ...
Added: January 8, 2014
Pavlov A., Mathematische Zeitschrift 2021 No. 297 P. 223-254
We show that for maximal Cohen–Macaulay modules over the homogeneous coordinate ring of a smooth Calabi–Yau varieties X, the computation of Betti numbers can be reduced to computations of dimensions of certain HomHom spaces in the bounded derived category Db(X). In the simplest case of a smooth elliptic curve E embedded in P2 as a smooth cubic, we get explicit values for Betti ...
Added: October 31, 2020
Brown F., / arxive. Series math "nt". 2013. No. 1110.6917.
Abstract. We study the de Rham fundamental group of the configuration space
E (n) of n + 1 marked points on a complex elliptic curve E, and define multiple
elliptic polylogarithms. These are multivalued functions on E (n) with unipotent
monodromy, and are constructed by a general averaging procedure. We show
that all iterated integrals on E (n) , ...
Added: May 14, 2014
Takebe T., Kuroki G., Journal of Physics A: Mathematical and Theoretical 2001 Vol. 34 No. 11 P. 2403-2413
We construct a Gaudin type lattice model as the Wess-Zumino-Witten model on elliptic curves at the critical level. Bethe eigenvectors are obtained by the bosonisation technique. ...
Added: August 14, 2014
Bogomolov F. A., Fu H., European Journal of Mathematics 2018 Vol. 4 No. 2 P. 555-560
We construct pairs of elliptic curves over number fields with large intersection of projective torsion points. ...
Added: September 13, 2018
Lebedev P. A., Nesterenko A., Чебышевский сборник 2012 Т. 13 № 2 (42) С. 91-105
We consider different parallel algortihms for operations in prime fields and their applications for operations on points of elliptic curves. The work provides results for implementations of these algorithms on NVIDIA graphical processors. ...
Added: February 25, 2013
Nesterenko A., Пугачев А. В., Прикладная дискретная математика 2015 № 4 С. 56-71
A new hybrid encryption scheme based on ElGamal asymmetric encryption scheme with distributed secret keys is presented. The keys are used for defence against unauthorised intrusion of encrypted messages. The security of the scheme is based on elliptic curve discrete logarithm problem. The main feature of the scheme is the fact that plain message is ...
Added: March 14, 2016
Nesterenko A., Фундаментальная и прикладная математика 2010 Т. 16 № 6 С. 109-122
В работе рассматриваются алгоритмы поиска длин циклов в последовательностях. Приводится обоснование изложенных алгоритмов, сравнение оценок их трудоёмкости, а также результаты их практического применения для решения задачи дискретного логарифмирования в группе точек эллиптической кривой ...
Added: March 3, 2013
M. G. Rukavishnikova, Mathematical notes 2011 Vol. 90 No. 3 P. 418-430
We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients. ...
Added: July 20, 2015
Bogomolov F. A., Fu H., / Cornell University. Series arXiv "math". 2017.
We explicitly construct pairs of elliptic curves defined over the algebraic numbers with large intersection of projective torsion points. ...
Added: June 20, 2017
Smirnov E., М. : МЦНМО, 2022
В брошюре рассказывается о числовых фризах, определенных Дж. Конвеем и Д. Кокстером в 1970-х гг. Это таблицы целых чисел, построенные по некоторому комбинаторному правилу и обладающие рядом глубоких и неожиданных свойств. В частности, они нумеруются триангуляциями многоугольников, возникают в разложениях чисел в цепные дроби и связаны с соотношениями в модулярной группе. Брошюра написана по материалам ...
Added: August 19, 2022
Gutnik L., International Mathematical Forum 2013 Vol. 8 No. 28 P. 1385-1396
This is continuation of our article [4]. When F and G in [4] are constant sequences, we obtain continued fraction for zeta(3) parametrized by some family of points (F,G) on projective line. This family of points can be obtained if from full projective line would be removed some no more than countable nowhere dense exeptional ...
Added: January 8, 2014