Question

Is the infinite product $\prod_{i=0}^{\infty}(1+\frac{1}{2^{3^i}})$ transcendental?

score 196 · Answer 1 · 2026-03-27 19:10:17

196

Views

Is the infinite product $\prod_{i=0}^{\infty}(1+\frac{1}{2^{3^i}})$ transcendental?

Published on 27 Mar 2026 - 19:10

score 72 · Answer 2 · 2021-07-05 10:59:49

72

Views

For $K=\mathbb Q(\alpha,\beta)$ with $\beta^2=\alpha^3$ if $\beta \in \mathbb Q(\alpha)$, then $|K:\mathbb Q|$ is finite.

Published on 05 Jul 2021 - 10:59

score 35 · Answer 3 · 2026-03-27 02:02:52

35

Views

Explaining Algebraic Independence of $\delta$ and $\gamma$

Published on 27 Mar 2026 - 2:02

score 88 · Answer 4 · 2026-02-23 13:40:58

88

Views

Transcendental numbers are decidable: a proof?

Published on 23 Feb 2026 - 13:40

score 74 · Answer 5 · 2021-08-16 02:30:32

74

Views

A countable set of transcendentals

Published on 16 Aug 2021 - 2:30

score 577 · Answer 6 · 2026-03-26 12:57:56

577

Views

Books for transcendental number theory

Published on 26 Mar 2026 - 12:57

score 66 · Answer 7 · 2026-03-26 13:01:20

66

Views

Transcendence of Liouville-Like Numbers

Published on 26 Mar 2026 - 13:01

score 127 · Answer 8 · 2026-03-27 19:32:35

127

Views

Rectangles with side lengths proportional to transcendental numbers BESIDES $\varphi$

Published on 27 Mar 2026 - 19:32

score 222 · Answer 9 · 2026-02-23 13:05:02

222

Views

Can every transcendental number be expressed as the infinite sum of a quotient of two polynomials?

Published on 23 Feb 2026 - 13:05

score 52 · Answer 10 · 2021-09-25 17:24:04

Can transcendent degree of transcendent number be algebraic? (meaning can both $\alpha^{\beta}$ and $\beta^{\alpha}$ be algebraic)

score 94 · Answer 11 · 2021-09-25 21:47:14

94

Views

Where does the linear equation in the proof of solvability in elementary numbers in [Chow 1999] come from?

Published on 25 Sep 2021 - 21:47

score 34 · Answer 12 · 2026-03-26 12:53:39

34

Views

Is there any $p \in \mathbb{Q}[x,y]$ with x and y degree both at least 1 such that $p(\pi,e)$ is known to be irrational?

Published on 26 Mar 2026 - 12:53

score 92 · Answer 13 · 2021-10-13 20:43:30

92

Views

Showing there exists a countable subfield $F\subseteq\Bbb{R}$ such that if $x\in F$, $\sin(x)\in F$

Published on 13 Oct 2021 - 20:43

score 65 · Answer 14 · 2021-11-07 17:38:27

65

Views

Proof that $\mathbb{Q}(x) \not \subseteq \mathbb{Q}(x+i)$

Published on 07 Nov 2021 - 17:38

score 87 · Answer 15 · 2021-11-08 08:02:01

87

Views

If $F \leq\overline{\mathbb{Q}}(x)$ then either $F/\mathbb{Q}$ or $\overline{\mathbb{Q}}(x)/F$ is algebraic.

Published on 08 Nov 2021 - 8:02

List Question

Is the infinite product $\prod_{i=0}^{\infty}(1+\frac{1}{2^{3^i}})$ transcendental?

For $K=\mathbb Q(\alpha,\beta)$ with $\beta^2=\alpha^3$ if $\beta \in \mathbb Q(\alpha)$, then $|K:\mathbb Q|$ is finite.

Explaining Algebraic Independence of $\delta$ and $\gamma$

Transcendental numbers are decidable: a proof?

A countable set of transcendentals

Books for transcendental number theory

Transcendence of Liouville-Like Numbers

Rectangles with side lengths proportional to transcendental numbers BESIDES $\varphi$

Can every transcendental number be expressed as the infinite sum of a quotient of two polynomials?

Can transcendent degree of transcendent number be algebraic? (meaning can both $\alpha^{\beta}$ and $\beta^{\alpha}$ be algebraic)

Where does the linear equation in the proof of solvability in elementary numbers in [Chow 1999] come from?

Is there any $p \in \mathbb{Q}[x,y]$ with x and y degree both at least 1 such that $p(\pi,e)$ is known to be irrational?

Showing there exists a countable subfield $F\subseteq\Bbb{R}$ such that if $x\in F$, $\sin(x)\in F$

Proof that $\mathbb{Q}(x) \not \subseteq \mathbb{Q}(x+i)$

If $F \leq\overline{\mathbb{Q}}(x)$ then either $F/\mathbb{Q}$ or $\overline{\mathbb{Q}}(x)/F$ is algebraic.

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