Results 221 to 230 of about 2,483 (259)

Simultaneous Diophantine approximation on manifolds and Hausdorff dimension

Journal of Number Theory, 2003
Let M be an m-dimensional, Ck manifold in Rn, for any k, m, n ? ?, and for any t> 0 let Lt(M)={x?M : ?qx?<q-t for infinitely many q??}, where, for x?R, ?x? min{ x - i :i?Z}, and for x=(x1,?,xn)???n, ?X? = max{?x1pr,?,?xn?}. In this paper it will be
Bryan P Rynne
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Triangles in diophantine approximation

Journal of Number Theory, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Effective equidistribution for multiplicative Diophantine approximation on lines

Inventiones Mathematicae, 2019
Given any line in the plane, we strengthen the Littlewood conjecture by two logarithms for almost every point on the line, thereby generalising the fibre result of Beresnevich, Haynes, and Velani.
Sam Chow, Lei Yang
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DIOPHANTINE APPROXIMATION WITH GAUSSIAN PRIMES

, 2019
In this paper we prove that the exact analogue of the author’s work with real irrationals and rational primes (G. Harman, On the distribution of $\alpha p$ modulo one II, Proc. London Math. Soc.
G. Harman
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On a problem in diophantine approximation

Proceedings of the Indian Academy of Sciences - Section A, 1942
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Simultaneous Diophantine Approximation

Proceedings of the London Mathematical Society, 1952
Proof of the theorem: ``Let \(c > 46^{-1/4}\). Then, for every pair of real irrational numbers \(\alpha, \beta\), there exist infinitely many solutions \(p, q, r > 0\) of \(r(p-\alpha r)^2 < c\), \(r(q- \beta r)^2 < c\) in integers.'' This result slightly improves one by \textit{P. Mullender} [Ann. Math. (2) 52, 417-426 (1950; Zbl 0037.17102)].
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Simultaneous Diophantine Approximation

Canadian Journal of Mathematics, 1950
Summary of results. The principal result of this paper is as follows: given any set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that(0.11).Also, if n = 2, we can, given t, produce numbers z1 and z2 such that(0.12)This supersedes the results of Nils Pipping (Acta Aboensis, vol.
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Diophantine approximation with one prime of the form p = x2 + y2 + 1

Lithuanian Mathematical Journal, 2021
S. Dimitrov
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Inhomogeneous and simultaneous Diophantine approximation in beta dynamical systems

Journal of Mathematical Analysis and Applications, 2023
Yu-Feng Wu
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Note on Diophantine approximation

Mathematical Proceedings of the Cambridge Philosophical Society, 1952
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