List questions from diophantine-approximation

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Does Faltings's theorem imply the set of Diophantine equations are decidable?

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show that $\{ nq^{\frac{1}{3}} \} + \{ nq^{\frac{2}{3}} \} \geq Cn^{-\frac{1}{2}}$

Published on 17 Nov 2017 - 8:09

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Dirichlet approximation theorem proof

Published on 09 Dec 2017 - 0:18

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A problem about effective uniformly distribution

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Scope of Hurwitz's Theorem for Diophantine approximation

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M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

Published on 01 Jan 2018 - 10:19

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Intuition behind the irrationality measure

Published on 23 Feb 2026 - 8:00

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Estimating $\#\{\{\alpha k\} < 1/\sqrt{k} : k \leq n\}$ for irrational $\alpha$

Published on 13 Feb 2011 - 11:00

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Non trivial upper bound for an exponential sum

Published on 18 Feb 2011 - 10:58

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Can we make $\tan(x)$ arbitrarily close to an integer when $x\in \mathbb{Z}$?

Published on 27 Feb 2011 - 16:20

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Is $\sin^2 n$ bounded away from zero?

Published on 28 Mar 2011 - 7:34

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What is the sum of the squares of the differences of consecutive element of a Farey Sequence

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Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$

Published on 27 Jun 2011 - 18:18

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An experiment was performed n times. The exact success rate rounds to 85.8%. What is the minimum value of n?

Published on 24 Jul 2011 - 20:48

List Question

Integrals for semiconvergent approximations to $\pi$

Does Faltings's theorem imply the set of Diophantine equations are decidable?

show that $\{ nq^{\frac{1}{3}} \} + \{ nq^{\frac{2}{3}} \} \geq Cn^{-\frac{1}{2}}$

Dirichlet approximation theorem proof

A problem about effective uniformly distribution

Scope of Hurwitz's Theorem for Diophantine approximation

M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

Intuition behind the irrationality measure

Estimating $\#\{\{\alpha k\} < 1/\sqrt{k} : k \leq n\}$ for irrational $\alpha$

Non trivial upper bound for an exponential sum

Can we make $\tan(x)$ arbitrarily close to an integer when $x\in \mathbb{Z}$?

Is $\sin^2 n$ bounded away from zero?

What is the sum of the squares of the differences of consecutive element of a Farey Sequence

Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$

An experiment was performed n times. The exact success rate rounds to 85.8%. What is the minimum value of n?

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