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Results tagged with irrational-numbers
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user 43108
An irrational number is a real number that cannot be expressed in the form $\frac{n}{m}$ where $n$ and $m$ are integers.
7
votes
Irrationality of Dedekind zeta values
As with all motivic L-functions, irrationality of special values breaks into two rather different problems:
Critical values. In the case of Dedekind zeta functions, those are the even positive intege …
- 17.6k
15
votes
Accepted
Is it possible to know if $\log(\pi)$ is irrational or not since the $\log$ function is the ...
The irrationality of $\log \pi$ is an open problem (see for example this recent paper).
It is expected to be transcendental (page 34 of this slides by Michel Waldschmidt), and in fact this follows fr …
- 17.6k
4
votes
Accepted
Is there a fixed integer $n$ for which the difference :$\pi^n-\ e ^n$ is integer number?
The claim that $\pi$ and $e$ are known to be algebraically independent is incorrect, see for example this MO question.
The rationality of $\pi^n-e^n$ is a well-known open problem alredy for $n=1$, an …
- 17.6k