Results 31 to 40 of about 618,965 (192)
Distribution of Values of Quadratic Forms at Integral Points
, 2019 The number of lattice points in $d$-dimensional hyperbolic or elliptic shells $\{m ...
Buterus, Paul +3 more
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An Inhomogeneous Transference Principle and Diophantine Approximation
, 2008 In a landmark paper, D.Y. Kleinbock and G.A. Margulis established the fundamental Baker-Sprindzuk conjecture on homogeneous Diophantine approximation on manifolds. Subsequently, there has been dramatic progress in this area of research.
Beresnevich, Victor, Velani, Sanju
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On Hilbert's Tenth Problem [PDF]
, 2014 Using an iterated Horner schema for evaluation of diophantine polynomials, we define a partial $\mu$-recursive "decision" algorithm decis as a "race" for a first nullstelle versus a first (internal) proof of non-nullity for such a polynomial -- within a ...
Pfender, Michael
core
Cubic diophantine inequalities III
Periodica Mathematica Hungarica, 1996 This paper reports on the continuing investigation by the author of the distribution of the values of diagonal cubic forms in seven and eight variables [Mathematica 35, 51-58 (1988; Zbl 0659.10015) and J. Lond. Math. Soc. (2) 53, 1-18 (1996; Zbl 0858.11018)]. The results of the present paper are as follows.
openaire +4 more sources
Plank theorems and their applications: A survey
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
wiley +1 more source
Diophantine Inequalities as a Problem of Difference between Consecutive Primes [PDF]
, 2014 In the present paper, we have developed a method for solving \textit{diophantine inequalities} using their relationship with the \textit{difference between consecutive primes}.
Sidokhine, Felix
core
The Davenport–Heilbronn method: 80 years on
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
wiley +1 more source
Report on some recent advances in Diophantine approximation [PDF]
, 2009 A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as
Waldschmidt, Michel
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Modular diophantine inequalities and numerical semigroups [PDF]
Pacific Journal of Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rosales, J. C. +2 more
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
wiley +1 more source