Supercongruences using modular forms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912430442938368 |
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| author | Beukers, Frits |
| author_facet | Beukers, Frits |
| contents | Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very often these congruences turn out to hold modulo $p^2$ or even $p^3$. We call such congruences supercongruences and in the past 15 years an abundance of them have been discovered. In this paper we show that a large proportion of them can be explained by the use of modular functions and forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supercongruences using modular forms Beukers, Frits Number Theory Algebraic Geometry 11A07, 11B65, 11F03 Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very often these congruences turn out to hold modulo $p^2$ or even $p^3$. We call such congruences supercongruences and in the past 15 years an abundance of them have been discovered. In this paper we show that a large proportion of them can be explained by the use of modular functions and forms. |
| title | Supercongruences using modular forms |
| topic | Number Theory Algebraic Geometry 11A07, 11B65, 11F03 |
| url | https://arxiv.org/abs/2403.03301 |