On the efficient computation of Fourier coefficients of eta-quotients
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866915728770203648 |
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| author | Barquero-Sanchez, Adrian De Rasis, Juan Pablo Sirolli, Nicolás Villegas-Morales, Jean Carlos |
| author_facet | Barquero-Sanchez, Adrian De Rasis, Juan Pablo Sirolli, Nicolás Villegas-Morales, Jean Carlos |
| contents | The Fourier coefficients of a negative weight eta-quotient, in many particular cases, and after Sussman in general, are known to be expressible by Hardy-Ramanujan-Rademacher type series.
We show that the central terms of the coefficients of these series can be efficiently computed, showing that they can be expressed in terms of twisted Kloosterman sums, and that they satisfy multiplicativity relations; this extends the results from Lehmer for the partition function.
We also give explicit bounds for the tails of these series, needed for effectively computing the aforementioned Fourier coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the efficient computation of Fourier coefficients of eta-quotients Barquero-Sanchez, Adrian De Rasis, Juan Pablo Sirolli, Nicolás Villegas-Morales, Jean Carlos Number Theory 11L05, 11Y35, 11P82 (Primary) 11P55, 11F20 (Secondary) The Fourier coefficients of a negative weight eta-quotient, in many particular cases, and after Sussman in general, are known to be expressible by Hardy-Ramanujan-Rademacher type series. We show that the central terms of the coefficients of these series can be efficiently computed, showing that they can be expressed in terms of twisted Kloosterman sums, and that they satisfy multiplicativity relations; this extends the results from Lehmer for the partition function. We also give explicit bounds for the tails of these series, needed for effectively computing the aforementioned Fourier coefficients. |
| title | On the efficient computation of Fourier coefficients of eta-quotients |
| topic | Number Theory 11L05, 11Y35, 11P82 (Primary) 11P55, 11F20 (Secondary) |
| url | https://arxiv.org/abs/2504.01384 |