AbstractFor an arbitrary sequence {αn} of nonnegative real numbers there is no known necessary and sufficient condition that for almost all x (in the sense of Lebesgue measure) there are infinitely many fractions pq satisfying |x − pq| < αqq. With a restriction on {αn} weaker than any previously used, except in a recent result of Erdös, we solve this problem and the analogous problem where p and q are required to be relatively prime
AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same si...
AbstractBeginning with an improvement to Dirichlet's Theorem on simultaneous approximation, in this ...
Let sum _q#psi#(q) denote a divergent series, where 0<#psi#(q)#<=#1/2. It is proved that for a...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractFor an arbitrary sequence {αn} of nonnegative real numbers there is no known necessary and s...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irratio...
AbstractIt is shown that if an is an increasing sequence of reals satisfying certain (fairly mild) c...
AbstractIt is shown that if an is an increasing sequence of reals satisfying certain (fairly mild) c...
AbstractWe consider metric results for the asymptotic behavior of the number of solutions of Diophan...
Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real nu...
Let $1<14/5$, $lambda_1,lambda_2,lambda_3$ and $lambda_4$ be non-zero real numbers, not all of th...
AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same si...
AbstractBeginning with an improvement to Dirichlet's Theorem on simultaneous approximation, in this ...
Let sum _q#psi#(q) denote a divergent series, where 0<#psi#(q)#<=#1/2. It is proved that for a...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractFor an arbitrary sequence {αn} of nonnegative real numbers there is no known necessary and s...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irratio...
AbstractIt is shown that if an is an increasing sequence of reals satisfying certain (fairly mild) c...
AbstractIt is shown that if an is an increasing sequence of reals satisfying certain (fairly mild) c...
AbstractWe consider metric results for the asymptotic behavior of the number of solutions of Diophan...
Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real nu...
Let $1<14/5$, $lambda_1,lambda_2,lambda_3$ and $lambda_4$ be non-zero real numbers, not all of th...
AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same si...
AbstractBeginning with an improvement to Dirichlet's Theorem on simultaneous approximation, in this ...
Let sum _q#psi#(q) denote a divergent series, where 0<#psi#(q)#<=#1/2. It is proved that for a...
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