Results 151 to 160 of about 14,956 (174)
Some of the next articles are maybe not open access.
Simultaneous Diophantine Approximation
Proceedings of the London Mathematical Society, 1952Proof 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)].
openaire +2 more sources
Sugaku Expositions, 2021
This article gives an introductory survey of recent progress on Diophantine problems, especially consequences coming from Schmidt’s subspace theorem, Baker’s transcendence method and Padé approximation. We present fundamental properties around Diophantine approximation and how it yields results in number theory.
openaire +2 more sources
This article gives an introductory survey of recent progress on Diophantine problems, especially consequences coming from Schmidt’s subspace theorem, Baker’s transcendence method and Padé approximation. We present fundamental properties around Diophantine approximation and how it yields results in number theory.
openaire +2 more sources
Simultaneous Diophantine Approximation
Canadian Journal of Mathematics, 1950Summary 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.
openaire +1 more source
1998
Abstract Dirichlet’s theorem. Khintchine’s theorem. The Duffin-Schaeffer results and conjecture. The Erdoős--Vaaler theorem. The zero-one laws of Cassels and Gallagher. CasselsΣ,-sequences. A crucial lemma ( Lemma 2.3). Overlap estimates. Reduction to GCD sums. Lacunary sequences.
openaire +1 more source
Abstract Dirichlet’s theorem. Khintchine’s theorem. The Duffin-Schaeffer results and conjecture. The Erdoős--Vaaler theorem. The zero-one laws of Cassels and Gallagher. CasselsΣ,-sequences. A crucial lemma ( Lemma 2.3). Overlap estimates. Reduction to GCD sums. Lacunary sequences.
openaire +1 more source
2000
Abstract A vector (q, Pl, … , Pn) ∈ zn+l, q ≥ 1, is called an approximation of order η ifThe number η(x) defined bysup has infinitely many solutions} is called the Diophantine approximation exponent.
openaire +1 more source
Abstract A vector (q, Pl, … , Pn) ∈ zn+l, q ≥ 1, is called an approximation of order η ifThe number η(x) defined bysup has infinitely many solutions} is called the Diophantine approximation exponent.
openaire +1 more source
Triangles in diophantine approximation
Journal of Number Theory, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Simultaneous asymptotic Diophantine approximations
Mathematika, 1967Let θ 1 , …, θ k be k real numbers. Suppose ψ( t ) is a positive decreasing function of the positive variable t . Define λ( N ), for all positive integers N , to be the number of solutions in integers p 1 …, p k , q of the inequalities ...
openaire +2 more sources
Simultaneous Diophantine Approximation
Journal of the London Mathematical Society, 1955openaire +2 more sources