Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distribution modulo one and denominators of the Bernoulli polynomials   Let $\{\cdot\}$ denote the fractional part and $n \geq 1$ be a fixed integer.
In this short note, we show for any prime $p$ the one-to-one correspondence
$$\sum_{\nu \geq 1} \left\{\frac{n}{p^\nu}\right\} > 1 \quad \iff \quad p \mid
\mathrm{denom}( B_n(x) - B_n ),$$ where $B_n(x) - B_n$ is the $n$th Bernoulli
polynomial without constant term and $\mathrm{denom}(\cdot)$ is its
denominator, which is squarefree.

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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: q-fin