Sign-patterns of Certain Infinite Products
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909699831496704 |
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| author | Huang, Zeyu Huber, Timothy McLaughlin, James Wang, Pengjun Xu, Yan Ye, Dongxi |
| author_facet | Huang, Zeyu Huber, Timothy McLaughlin, James Wang, Pengjun Xu, Yan Ye, Dongxi |
| contents | The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for the coefficient sign patterns for \[ \frac{(q^i;q^i)_{\infty}}{(q^p;q^p)_{\infty}} \] for integers \( i > 1 \) and primes \( p > 3 \). The sign analysis for this quotient addresses and extends a conjecture of Bringmann et al. for the coefficients of \( (q^2;q^2)_{\infty}(q^5;q^5)_{\infty}^{-1} \). The sign distribution for additional classes of eta quotients is considered. This addresses multiple conjectures posed by Bringmann et al. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sign-patterns of Certain Infinite Products Huang, Zeyu Huber, Timothy McLaughlin, James Wang, Pengjun Xu, Yan Ye, Dongxi Number Theory 11F30 (Primary) 30C50 (Secondary) The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for the coefficient sign patterns for \[ \frac{(q^i;q^i)_{\infty}}{(q^p;q^p)_{\infty}} \] for integers \( i > 1 \) and primes \( p > 3 \). The sign analysis for this quotient addresses and extends a conjecture of Bringmann et al. for the coefficients of \( (q^2;q^2)_{\infty}(q^5;q^5)_{\infty}^{-1} \). The sign distribution for additional classes of eta quotients is considered. This addresses multiple conjectures posed by Bringmann et al. |
| title | Sign-patterns of Certain Infinite Products |
| topic | Number Theory 11F30 (Primary) 30C50 (Secondary) |
| url | https://arxiv.org/abs/2507.16644 |