Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $b$-ary expansions of $\log (1 + \frac{1}{a})$ and ${\mathrm e}$   Let $b \ge 2$ be an integer and $\xi$ an irrational real number. We prove
that, if the irrationality exponent of $\xi$ is equal to $2$ or slightly
greater than $2$, then the $b$-ary expansion of $\xi$ cannot be `too simple',
in a suitable sense. Our result applies, among other classical numbers, to
badly approximable numbers, non-zero rational powers of ${\mathrm e}$, and
$\log (1 + \frac{1}{a})$, provided that the integer $a$ is sufficiently large.
It establishes an unexpected connection between the irrationality exponent of a
real number and its $b$-ary expansion.

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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th