On the multiplicative pair correlations of sums of two squares
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912903419920384 |
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| author | Parkkonen, Jouni Paulin, Frédéric |
| author_facet | Parkkonen, Jouni Paulin, Frédéric |
| contents | We study the pair correlations of the logarithms of the integral values of quadratic norm forms at various scalings, proving the existence of pair correlation measures. We describe a surprising set of asymptotic behaviours when the scaling increases, passing from a punctual measure to a Poissonian behaviour through an exotic behaviour at the transition phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13058 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the multiplicative pair correlations of sums of two squares Parkkonen, Jouni Paulin, Frédéric Number Theory We study the pair correlations of the logarithms of the integral values of quadratic norm forms at various scalings, proving the existence of pair correlation measures. We describe a surprising set of asymptotic behaviours when the scaling increases, passing from a punctual measure to a Poissonian behaviour through an exotic behaviour at the transition phase. |
| title | On the multiplicative pair correlations of sums of two squares |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.13058 |