Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform Convergence Behavior of the Bernoulli Polynomials   The roots of Bernoulli polynomials, $B_n(z)$, when plotted in the complex
plane, accumulate around a peculiar H-shaped curve. Karl Dilcher proved in 1987
that, on compact subsets of $\mathbb{C}$, the Bernoulli polynomials
asymptotically behave like sine or cosine. Here we establish the asmptotic
behavior of $B_n(nz)$, compute the distribution of real roots of Bernoulli
polynomials and show that, properly rescaled, the complex roots lie on the
curve $e^{- 2\pi \text{Im}(z)} = 2\pi e |z|$ or $e^{2\pi \text{Im}(z)}= 2\pi e
|z|$.

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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an