Spectral Tile Direction in the Group $\mathbb{Z}_{p^2} \times \mathbb{Z}_{q^2} \times \mathbb{Z}_r$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915042878816256 |
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| author | Fallon, Thomas Kiss, Gergely Mayeli, Azita Somlai, Gábor |
| author_facet | Fallon, Thomas Kiss, Gergely Mayeli, Azita Somlai, Gábor |
| contents | In this paper, we investigate Fuglede's conjecture for $\mathbb{Z}_{p^2q^2r}$ and provide a proof under the condition $p^2q^2 \leq r$. We develop a new technique by analyzing the divisibility of the mask polynomial of a given set by a system of cyclotomic polynomials. Combined with the so-called mod-$p$-method, this technique serves as a powerful tool for studying Fuglede's conjecture in this and related cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16277 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral Tile Direction in the Group $\mathbb{Z}_{p^2} \times \mathbb{Z}_{q^2} \times \mathbb{Z}_r$ Fallon, Thomas Kiss, Gergely Mayeli, Azita Somlai, Gábor Classical Analysis and ODEs Group Theory Number Theory 43A40, 43A75, 52C22, 05B25 In this paper, we investigate Fuglede's conjecture for $\mathbb{Z}_{p^2q^2r}$ and provide a proof under the condition $p^2q^2 \leq r$. We develop a new technique by analyzing the divisibility of the mask polynomial of a given set by a system of cyclotomic polynomials. Combined with the so-called mod-$p$-method, this technique serves as a powerful tool for studying Fuglede's conjecture in this and related cases. |
| title | Spectral Tile Direction in the Group $\mathbb{Z}_{p^2} \times \mathbb{Z}_{q^2} \times \mathbb{Z}_r$ |
| topic | Classical Analysis and ODEs Group Theory Number Theory 43A40, 43A75, 52C22, 05B25 |
| url | https://arxiv.org/abs/2308.16277 |