The denominators of power sums of arithmetic progressions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866929399136256000 |
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| author | Kellner, Bernd C. Sondow, Jonathan |
| author_facet | Kellner, Bernd C. Sondow, Jonathan |
| contents | In a recent paper the authors studied the denominators of polynomials that represent power sums by Bernoulli's formula. Here we extend our results to power sums of arithmetic progressions. In particular, we obtain a simple explicit criterion for integrality of the coefficients of these polynomials. As applications, we obtain new results on the sequence of denominators of the Bernoulli polynomials. A consequence is that certain quotients of successive denominators are infinitely often integers, which we characterize. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_05331 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | The denominators of power sums of arithmetic progressions Kellner, Bernd C. Sondow, Jonathan Number Theory 11B68, 11B83 In a recent paper the authors studied the denominators of polynomials that represent power sums by Bernoulli's formula. Here we extend our results to power sums of arithmetic progressions. In particular, we obtain a simple explicit criterion for integrality of the coefficients of these polynomials. As applications, we obtain new results on the sequence of denominators of the Bernoulli polynomials. A consequence is that certain quotients of successive denominators are infinitely often integers, which we characterize. |
| title | The denominators of power sums of arithmetic progressions |
| topic | Number Theory 11B68, 11B83 |
| url | https://arxiv.org/abs/1705.05331 |