Question

How to recover a number from approximation

score 60 · Answer 1 · 2020-01-26 16:23:11

60

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How to recover a number from approximation

Published on 26 Jan 2020 - 16:23

score 293 · Answer 2 · 2020-01-30 18:18:01

293

Views

$\{mb + n \mid b\in \mathbb{R} \setminus \mathbb{Q} \text{ and } m, n \in \mathbb{Z} \}$ is dense in $\mathbb{R}$

Published on 30 Jan 2020 - 18:18

score 62 · Answer 3 · 2020-02-11 20:49:24

62

Views

Waring's problem for sum of squares -- $\sqrt{2}$ does not lie in a minor arc

Published on 11 Feb 2020 - 20:49

score 454 · Answer 4 · 2020-02-15 20:40:00

454

Views

Diophantine properties of $\log(3)/\log(2)$ (and other questions)

Published on 15 Feb 2020 - 20:40

score 103 · Answer 5 · 2026-03-25 11:00:46

103

Views

Can $q^2 \alpha \,(\text{mod } 1)$ be made arbitrarily small?

Published on 25 Mar 2026 - 11:00

score 86 · Answer 6 · 2020-03-23 09:44:13

86

Views

Asymptotic expansion for $a_n=\inf_{1\leq k \leq n}|\sin(k)|$

Published on 23 Mar 2020 - 9:44

score 103 · Answer 7 · 2020-03-26 19:04:18

103

Views

Fractional parts of integral multiples of an irrational number

Published on 26 Mar 2020 - 19:04

score 677 · Answer 8 · 2020-03-27 04:49:22

677

Views

Prove that the Pell's Equation $x^2 −Dy^2 = 1$ always has a solution where $y$ is a multiple of $41$

Published on 27 Mar 2020 - 4:49

score 133 · Answer 9 · 2020-04-04 02:56:05

133

Views

On Littlewood Conjecture

Published on 04 Apr 2020 - 2:56

score 228 · Answer 10 · 2020-04-20 19:07:33

228

Views

Dirichlet approximation theorem: How "sporadic" are the good denominators?

Published on 20 Apr 2020 - 19:07

score 107 · Answer 11 · 2020-05-13 23:51:34

107

Views

Reconciling Liouville’s theorem and Dirichlet's theorem

Published on 13 May 2020 - 23:51

score 54 · Answer 12 · 2020-05-15 23:32:19

54

Views

What can be said about this "modified" irrationality measure?

Published on 15 May 2020 - 23:32

score 319 · Answer 13 · 2020-05-17 03:59:52

319

Views

Does the set of real numbers with bounded partial quotients have positive measure?

Published on 17 May 2020 - 3:59

score 121 · Answer 14 · 2020-05-18 03:36:54

121

Views

Is the set of "good exponents" in Diophantine approximation closed?

Published on 18 May 2020 - 3:36

score 256 · Answer 15 · 2020-05-19 06:52:46

256

Views

Show that an irrational square root of an integer is a badly approximable number.

Published on 19 May 2020 - 6:52

List Question

How to recover a number from approximation

$\{mb + n \mid b\in \mathbb{R} \setminus \mathbb{Q} \text{ and } m, n \in \mathbb{Z} \}$ is dense in $\mathbb{R}$

Waring's problem for sum of squares -- $\sqrt{2}$ does not lie in a minor arc

Diophantine properties of $\log(3)/\log(2)$ (and other questions)

Can $q^2 \alpha \,(\text{mod } 1)$ be made arbitrarily small?

Asymptotic expansion for $a_n=\inf_{1\leq k \leq n}|\sin(k)|$

Fractional parts of integral multiples of an irrational number

Prove that the Pell's Equation $x^2 −Dy^2 = 1$ always has a solution where $y$ is a multiple of $41$

On Littlewood Conjecture

Dirichlet approximation theorem: How "sporadic" are the good denominators?

Reconciling Liouville’s theorem and Dirichlet's theorem

What can be said about this "modified" irrationality measure?

Does the set of real numbers with bounded partial quotients have positive measure?

Is the set of "good exponents" in Diophantine approximation closed?

Show that an irrational square root of an integer is a badly approximable number.

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