# Tagged Questions

**4**

votes

**1**answer

150 views

### Hermite Lindemann and transcendental reals

This is about compass and straightedge constructions, although I suspect nothing changes if we expand to real numbers algebraic over the rationals.
Anyway, let $E$ be the "constructible numbers," ...

**10**

votes

**2**answers

404 views

### Numbers with known finite irrationality measure greater than 2

For a real number $\alpha$, let the irrationality measure $\mu(\alpha) \in \mathbb{R}\cup \{\infty\}$ be defined as the supremum of all real numbers $\mu$ such that
$$ \left| ...

**11**

votes

**2**answers

2k views

### Why is it hard to prove that the Euler Mascheroni constant is irrational?

Philosophically why should proving that $\gamma$ is irrational (let alone transcendental) be so much harder than proving $\pi$ or $e$ are irrational?

**20**

votes

**1**answer

996 views

### Is this seemingly novel irrational constant also transcendental?

I recently discovered a constant that is constructed as follows:
$\chi=\sum_{n=1}^\infty (\frac{\cos{n}}{2|\cos{n}|}+\frac{1}{2}) 2^{-n}$
Furthermore I can prove that it is an irrational number ...

**9**

votes

**0**answers

451 views

### Connections of results in Harmonic analysis in the theory of Transcendental Numbers

An entire function $f$ is said to be of exponential type if there exist constants $c$ and $k$ such that $|f(z)|\leq c e^{k |z|}$.
A famous result of Polya says if $f$ is an entire function of ...

**3**

votes

**2**answers

508 views

### Is this number already known to be transcendental? Is there a survey about up-to-date trascendence results?

Is the number $\sum_{n=1}^\infty \frac{1}{2^{n^2}}$ known to be transcendental?
Is there a survey with up-to-date transcendence results?