AbstractLet β be an irrational number. For t ≥ 1, put ψβ(t)= minp,qint 0<q⩽t | qβ − p |, μ∗(β)= supt⩾1 tψβ(t) and write μ∗(β) = Rβ∗(1 + Rβ∗). Further, denote by M∗ the set of all values Rβ∗ when β runs over all irrational numbers. The author proves that M∗ contains a sequence of elements between 1 + √5 and 2 + √5 tending to 2 + √5 but does not contain 2 + √5 itself and that a number R∗∗ exists such that the whole interval [R∗∗, ∞] ⊂ M∗
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
Arealnumberβ>1 is said to satisfy Property (F) if every non-negative number of Z[β −1] has a fini...
The ordinary continued fractions expansion of a real number is based on the Euclidean division. Vari...
AbstractFor irrational numbers θ define α(θ) = lim sup{1/(q(p − qθ))|p ∈ Z, q ∈ N, p − qθ > 0} and α...
AbstractLet β be an irrational number. For t ≥ 1, put ψβ(t)= minp,qint 0<q⩽t | qβ − p |, μ∗(β)= supt...
The irrationality exponent a of a real number x is the supremum of the set of real numbers z for whi...
on the occasion of his 60th birthday Abstract. — Let α> 1 be irrational. Several authors studied ...
AbstractLet ξ be a real irrational number, and φ be a function (satisfying some assumptions). In thi...
We prove that if q is an integer greater than one and r is a non-zero rational (r≠−qm) then Σn=1∞ (1...
AbstractLet ξ be an irrational number with simple continued fraction expansion ξ = [a0; a1, a2, ...,...
AbstractFor an irrational number x and n⩾1, we denote by kn(x) the exact number of partial quotients...
We present a hypergeometric construction of rational approximations to ζ(2) and ζ(3) which allows on...
In 1978, Apéry [2] proved the irrationality of ζ(3) by constructing two explicit sequences of integ...
AbstractFor any real number β>1, let ε(1,β)=(ε1(1),ε2(1),…,εn(1),…) be the infinite β-expansion of 1...
A reasonably complete theory of the approximation of an irrational by rational fractions whose numer...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
Arealnumberβ>1 is said to satisfy Property (F) if every non-negative number of Z[β −1] has a fini...
The ordinary continued fractions expansion of a real number is based on the Euclidean division. Vari...
AbstractFor irrational numbers θ define α(θ) = lim sup{1/(q(p − qθ))|p ∈ Z, q ∈ N, p − qθ > 0} and α...
AbstractLet β be an irrational number. For t ≥ 1, put ψβ(t)= minp,qint 0<q⩽t | qβ − p |, μ∗(β)= supt...
The irrationality exponent a of a real number x is the supremum of the set of real numbers z for whi...
on the occasion of his 60th birthday Abstract. — Let α> 1 be irrational. Several authors studied ...
AbstractLet ξ be a real irrational number, and φ be a function (satisfying some assumptions). In thi...
We prove that if q is an integer greater than one and r is a non-zero rational (r≠−qm) then Σn=1∞ (1...
AbstractLet ξ be an irrational number with simple continued fraction expansion ξ = [a0; a1, a2, ...,...
AbstractFor an irrational number x and n⩾1, we denote by kn(x) the exact number of partial quotients...
We present a hypergeometric construction of rational approximations to ζ(2) and ζ(3) which allows on...
In 1978, Apéry [2] proved the irrationality of ζ(3) by constructing two explicit sequences of integ...
AbstractFor any real number β>1, let ε(1,β)=(ε1(1),ε2(1),…,εn(1),…) be the infinite β-expansion of 1...
A reasonably complete theory of the approximation of an irrational by rational fractions whose numer...
AbstractThe function f(θ, φ; x, y) = Σk = 1∞ Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ i...
Arealnumberβ>1 is said to satisfy Property (F) if every non-negative number of Z[β −1] has a fini...
The ordinary continued fractions expansion of a real number is based on the Euclidean division. Vari...
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