On the rate of convergence to zero of the measure of extremal sets in metric theory of transcendental numbers

Budarina, Natalia

doi:10.1007/s00209-018-2211-1

Math. Z.

2018

DOI: 10.1007/s00209-018-2211-1

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On the rate of convergence to zero of the measure of extremal sets in metric theory of transcendental numbers

Natalia Budarina

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Cited by 4 publications

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“…The question of establishing the rate of convergence to zero of the measure of the set L n (Q, w) is very natural. The first significant contribution to obtaining an effective estimate for the measure of the set L n (Q, w) was made in [14] and it was shown that μ(L n (Q, w)) Q −(w−n)/n μ(I),…”

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confidence: 99%

Quantitative Estimate for the Measure of a Set of Real Numbers

Budarina¹

2021

Glasgow Math. J.

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confidence: 99%

Quantitative Estimate for the Measure of a Set of Real Numbers

Budarina¹

2021

Glasgow Math. J.

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An effective estimate for the measure of the set of p-adic numbers with a given order of approximation

Budarina

2019

Int. J. Number Theory

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Diophantine approximation with the constant right-hand side of inequalities on short intervals

2021

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In the metric theory of Diophantine approximations, one of the main problems leading to exact characteristics in the classifications of Mahler and Koksma is to estimate the Lebesgue measure of the points x ∈ B ⊂ I from the interval I such as the inequality | P (x) | < Q-w, w > n, Q >1 for the polynomials P(x) ∈ Z[x], deg P ≤ n, H(P) ≤Q is satisfied. The methods of obtaining estimates are different at different intervals of w change. In this article, at w > n +1 we get the estimate µ B< c1(n) Q – (w-1/n). The best estimate to date was c2(n) Q –(w- n/n).

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On the rate of convergence to zero of the measure of extremal sets in metric theory of transcendental numbers

Cited by 4 publications

References 10 publications

Quantitative Estimate for the Measure of a Set of Real Numbers

Quantitative Estimate for the Measure of a Set of Real Numbers

An effective estimate for the measure of the set of p-adic numbers with a given order of approximation

Diophantine approximation with the constant right-hand side of inequalities on short intervals

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