The asymptotics for the number of real roots of the Bernoulli polynomials

A. Efimov

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The asymptotics for the number of real roots of the Bernoulli polynomials

A. Efimov

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Abstract

A new short clear proof of the asymptotics for the number $c_n$ of real roots of the Bernoulli polynomials $B_n(x)$, as well as for the maximal root $y_n$: $$y_n=\frac{n}{2\pi e}+\frac{\ln(n)}{4\pi e}+O(1)\quad\text{and}\quad c_n=\frac{2n}{\pi e}+\frac{\ln(n)}{\pi e}+O(1).$$

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A. Efimov. 2006-06-15. The asymptotics for the number of real roots of the Bernoulli polynomials. https://arxiv.org/abs/math/0606361

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