Results 1 to 10 of about 14,956 (174)
Best Simultaneous Diophantine Approximations under a Constraint on the Denominator [PDF]
, 2005 We investigate the problem of best simultaneous Diophantine approximation under a constraint on the denominator, as proposed by Jurkat. New lower estimates for optimal approximation constants are given in terms of critical determinants of suitable star ...
Aliev, Iskander, Gruber, Peter
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Restricted simultaneous Diophantine approximation [PDF]
Mathematika, 2016 We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.Comment: 16 pages.
Baier, Stephan, Ghosh, Anish
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Diophantine approximation and coloring [PDF]
The American Mathematical Monthly, 2014 We demonstrate how connections between graph theory and Diophantine approximation can be used in conjunction to give simple and accessible proofs of seemingly difficult results in both subjects.Comment: 16 pages, pre-publication version of paper which ...
Haynes, Alan, Munday, Sara
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DIOPHANTINE APPROXIMATION BY PRIMES [PDF]
Glasgow Mathematical Journal, 2009 AbstractWe show that whenever δ > 0 and constants λisatisfy some necessary conditions, there are infinitely many prime triplesp1,p2,p3satisfying the inequality |λ0+ λ1p1+ λ2p2+ λ3p3| < (maxpj)−2/9+δ. The proof uses Davenport–Heilbronn adaption of the circle method together with a vector sieve method.
Kaisa Matomäki
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Simultaneous Diophantine approximation
Duke Mathematical Journal, 1946 The simplest problems of Diophantine approximation relate to the approximation of a single irrational number 0 by rational numbers pjq, and the principal question is how small we can make the error 0 — pjq in relation to q for infinitely many approximations. It is well known that this question can be answered almost completely in terms of the continued
Davenport, H., Mahler, K.
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Metrical Diophantine approximation for quaternions [PDF]
, 2014 Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.Comment: 30 pages.
Beresnevich +27 more
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Restricted diophantine approximation [PDF]
Journal of the Australian Mathematical Society, 1977 AbstractThe problem considered is that of approximating irrationals α by rationals p/q where p and q avoid certain congruence classes mod 2k for certain integers k. Results are obtained which give close bounds on a number c such that |α - p/q| < c/q2 has infinitely many solutions where p and q can be expressed as the sum of three squares.
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Failure of strong approximation on an affine cone [PDF]
, 2018 We use the Brauer-Manin obstruction to strong approximation on a punctured affine cone to explain a curious property of coprime integer solutions to a homogeneous Diophantine equation.Comment: Changes following referee's ...
Bright, Martin, Kok, Ivo
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Simultaneous diophantine approximation [PDF]
Bulletin of the Australian Mathematical Society, 1972 AbstractUsing a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394.
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Diophantine approximation on lines with prime constraints
, 2013 We study the problem of Diophantine approximation on lines in R^2 with prime numerator and denominator.Comment: 14 ...
Baier, Stephan, Ghosh, Anish
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