AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free sequences of “good” Diophantine approximations to a fixed α ∈ C are trivial ones. For example, suppose that a > 1 and that (δn)n=1∞ and (σn)n=1∞ are two positive, strictly increasing unbounded sequences satisfying δn+1 ≤ aδn and σn+1 ≤ aσn. If there is a sequence of nonzero polynomials Pn ∈ Z[x] with deg Pn ≤ δn, deg Pn + log height Pn ≤ σn, and ∣Pn(α)∣ ≤ e−(2a+1)δnσn, then each Pn(α) = 0
Diophantine approximation is traditionally the study of how well real numbers are approximated by ra...
AbstractWe show how Padé approximations are used to get Diophantine approximations of real or comple...
In the article we present in the Mizar system [1], [2] the formalized proofs for Hurwitz’ theorem [4...
AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free seque...
For K a cubic field with only one real embedding and α, β ϵ K, we show how to construct an increasin...
AbstractAnswering a question of Liardet, we prove that if 1,α1,α2,…,αt are real numbers linearly ind...
A theory is presented for simultaneous Diophantine approximation by means of minimal sets of lattice...
AbstractLower bounds are obtained on the simultaneous diophantine approximation of some values of ce...
AbstractBeginning with an improvement to Dirichlet's Theorem on simultaneous approximation, in this ...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irratio...
Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote th...
Abstract. We give a sufficient and necessary condition such that for almost all s ∈ R ‖nθ − s ‖ <...
Diophantine approximation is traditionally the study of how well real numbers are approximated by ra...
AbstractWe show how Padé approximations are used to get Diophantine approximations of real or comple...
In the article we present in the Mizar system [1], [2] the formalized proofs for Hurwitz’ theorem [4...
AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free seque...
For K a cubic field with only one real embedding and α, β ϵ K, we show how to construct an increasin...
AbstractAnswering a question of Liardet, we prove that if 1,α1,α2,…,αt are real numbers linearly ind...
A theory is presented for simultaneous Diophantine approximation by means of minimal sets of lattice...
AbstractLower bounds are obtained on the simultaneous diophantine approximation of some values of ce...
AbstractBeginning with an improvement to Dirichlet's Theorem on simultaneous approximation, in this ...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ t...
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irratio...
Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote th...
Abstract. We give a sufficient and necessary condition such that for almost all s ∈ R ‖nθ − s ‖ <...
Diophantine approximation is traditionally the study of how well real numbers are approximated by ra...
AbstractWe show how Padé approximations are used to get Diophantine approximations of real or comple...
In the article we present in the Mizar system [1], [2] the formalized proofs for Hurwitz’ theorem [4...
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