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A strengthening of a theorem of Bourgain and Kontorovich
Izvestiya. Mathematics. 2014. Vol. 78. No. 2. P. 293-353.
Kan I. D.
We prove that positive integers contains a positive proportion of numbers, satisfying Zaremba's conjecture with A=7.
This result is a strengthening of a similar theorem of Bourgain-Kontorovich, obtained for A=50.
Priority areas:
mathematics
Language:
English
Кан И. Д., Frolenkov D., Известия РАН. Серия математическая 2014 Т. 78 № 2 С. 87-144
We prove that the set of positive integers contains a positive proportion of numbers satisfying Zaremba’s conjecture withA= 7. This result strengthens a similar theorem of Bourgain and Kontorovich obtained for A= 50. ...
Added: October 23, 2014
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
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
Makarov I., Mathematical notes 2014 Vol. 95 No. 6 P. 795-805
The convex hull of all integer points of a noncompact polyhedron is closed and is a generalized polyhedron only under certain conditions. It is proved that if only the integer points in the interior of the polyhedron are taken, then most of the conditions can be dropped. Moreover, the object thus obtained has properties resembling ...
Added: June 9, 2014
Рукавишникова М. Г., Чебышевский сборник 2006 Т. 7 № 4 С. 113-121
a ...
Added: July 20, 2015
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
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
Gutnik L., International Mathematical Forum 2013 Vol. 17 No. 6 P. 771-781
We found a series of continued fractions for zeta(3), parametrized by some family of pairs of sequences F,G. Two members of this series are present here; they are different from Apery-Nesterenko continued fraction. ...
Added: May 17, 2013
Nesterenko A., 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. ...
Added: February 2, 2015
Frolenkov D., Известия РАН. Серия математическая 2012 Т. 76 № 4 С. 125-184
We get an asymptotic formula for the mean value of Frobenius numbers wiyh three arguments when averaged with respect to three parameters ...
Added: November 1, 2014
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
Gutnik L., Advances in Difference Equations 2010 No. Article ID 143521 P. 1-11
Yu. V. Nesterenko has proved that ζ_3_ _ b0 _ a1|/|b1 _ · · · _ aν|/|bν _ · · · , b0 _ b1 _ a2 _ 2,
a1 _ 1, b2 _ 4, b4k_1 _ 2k _ 2, a4k_1 _ k_k _ 1_, b4k_2 _ 2k _ 4, and a4k_2 _ _k _ 1__k ...
Added: November 11, 2013
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
Kalmynin A. B., Mathematical notes 2016 Vol. 99 No. 3 P. 470-476
Added: July 7, 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
Feigin E., European Journal of Combinatorics 2012 Vol. 33 No. 1 P. 1913-1918
It has been shown recently that the normalized median Genocchi numbers are equal to the Euler characteristics of the degenerate flag varieties. The q-analogues of the Genocchi numbers can be naturally defined as the Poincare polynomials of the degenerate flag varieties. We prove that the generating function of the Poincare polynomials can be written as ...
Added: July 18, 2012
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013
Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
Added: February 5, 2014
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
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Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240
We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
Added: February 9, 2019