Beukers-like proofs of irrationality for $ζ{(2)}$ and $ζ{(3)}$
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arXiv
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| Format: | Preprint |
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2013
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| _version_ | 1866908948316028928 |
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| author | Lima, F. M. S. |
| author_facet | Lima, F. M. S. |
| contents | In this note, I develop step-by-step proofs of irrationality for $\,ζ{(2)}\,$ and $\,ζ{(3)}$. Though the proofs follow closely those based upon unit-square integrals proposed originally by Beukers, I introduce some modifications which certainly will be useful for those interested in understanding this kind of proof and/or trying to extend it to higher zeta values, Catalan's constant, or other related numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1308_2720 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Beukers-like proofs of irrationality for $ζ{(2)}$ and $ζ{(3)}$ Lima, F. M. S. Number Theory 11J72, 11J82, 11M06 In this note, I develop step-by-step proofs of irrationality for $\,ζ{(2)}\,$ and $\,ζ{(3)}$. Though the proofs follow closely those based upon unit-square integrals proposed originally by Beukers, I introduce some modifications which certainly will be useful for those interested in understanding this kind of proof and/or trying to extend it to higher zeta values, Catalan's constant, or other related numbers. |
| title | Beukers-like proofs of irrationality for $ζ{(2)}$ and $ζ{(3)}$ |
| topic | Number Theory 11J72, 11J82, 11M06 |
| url | https://arxiv.org/abs/1308.2720 |