The asymptotics for the number of real roots of the Bernoulli polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2006
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| _version_ | 1866912222608883712 |
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| author | Efimov, A. |
| author_facet | Efimov, A. |
| contents | 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 $y_n$: $$y_n=\frac{n}{2πe}+\frac{\ln(n)}{4πe}+O(1)\quad\text{and}\quad c_n=\frac{2n}{πe}+\frac{\ln(n)}{πe}+O(1).$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0606361 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | The asymptotics for the number of real roots of the Bernoulli polynomials Efimov, A. Number Theory 11B68, 11B83 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 $y_n$: $$y_n=\frac{n}{2πe}+\frac{\ln(n)}{4πe}+O(1)\quad\text{and}\quad c_n=\frac{2n}{πe}+\frac{\ln(n)}{πe}+O(1).$$ |
| title | The asymptotics for the number of real roots of the Bernoulli polynomials |
| topic | Number Theory 11B68, 11B83 |
| url | https://arxiv.org/abs/math/0606361 |