Results 121 to 130 of about 2,483 (259)
Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
wiley +1 more source
Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations [PDF]
, 2005 summary:We prove an analogue of the convergence part of Khintchine’s theorem for the simultaneous inhomogeneous Diophantine approximation on the Veronese curve $(x,x^2,\ldots ,x^n)$ with respect to the different valuations.
Bernik, Vasily +7 more
core +1 more source
Mathematika, Volume 72, Issue 2, April 2026.Abstract In 2019 Kleinbock and Wadleigh proved a “zero‐one law” for uniform inhomogeneous Diophantine approximations. We generalize this statement to arbitrary weight functions and establish a new and simple proof of this statement, based on the transference principle. We also give a complete description of the sets of g$g$‐Dirichlet pairs with a fixed
Vasiliy Neckrasov
wiley +1 more source
Sequences of Diophantine approximations
Journal of Number Theory, 1974 AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free sequences of “good” Diophantine approximations to a fixed α ∈ C are trivial ones. For example, suppose that a > 1 and that (δn)n=1∞ and (σn)n=1∞ are two positive, strictly increasing unbounded sequences satisfying δn+1 ≤ aδn and σn+1 ≤ aσn.
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On the topology of Diophantine approximation spectra [PDF]
Compositio Mathematica, 2017 Fix an integer $n\geqslant 2$ . To each non-zero point $\mathbf{u}$
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Diophantine approximation in prescribed degree [PDF]
, 2017 We investigate approximation to a given real number by algebraic numbers and algebraic integers of prescribed degree. We deal with both best and uniform approximation, and highlight the similarities and differences compared with the intensely studied ...
J. Schleischitz
semanticscholar +1 more source
Distribution of integer points on determinant surfaces and a mod‐p analogue
Mathematika, Volume 72, Issue 2, April 2026.Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
wiley +1 more source
New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method
Cryptography, 2018 This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus N = p q in polynomial time. The paper has two parts.
Muhammad Rezal Kamel Ariffin +3 more
doaj +1 more source
A NOTE ON INHOMOGENEOUS DIOPHANTINE APPROXIMATION [PDF]
Glasgow Mathematical Journal, 2003 Let $\alpha$ be an irrational number. We determine the Hausdorff dimension of sets of real numbers which are close to infinitely many elements of the sequence $(\{n\alpha\})_{n\,{\ge}\,1}$.
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Metric Diophantine Approximation : aspects of recent work [PDF]
, 2016 In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approximation; such as theorems of Khintchine, Jarnik, Duffin-Schaeffer and Gallagher.
V. Beresnevich +2 more
semanticscholar +1 more source