The shape of quadratic Gauss paths
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914013903847424 |
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| author | Dell, Justine Milićević, Djordje |
| author_facet | Dell, Justine Milićević, Djordje |
| contents | We consider the distribution of quadratic Gauss paths, polygonal paths joining partial sums of quadratic Gauss sums to square-free fundamental discriminant moduli in a dyadic range [Q,2Q]. We prove that this striking ensemble converges in law, as Q->\infty, to a random Fourier series we explicitly describe, and we prove a convergence in probability result and a classification result for the limiting shapes that explain the visually remarkable properties of these Gauss paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The shape of quadratic Gauss paths Dell, Justine Milićević, Djordje Number Theory Probability 11L05 Primary, 11L40, 11N64, 60F17, 60G17, 60G50 Secondary We consider the distribution of quadratic Gauss paths, polygonal paths joining partial sums of quadratic Gauss sums to square-free fundamental discriminant moduli in a dyadic range [Q,2Q]. We prove that this striking ensemble converges in law, as Q->\infty, to a random Fourier series we explicitly describe, and we prove a convergence in probability result and a classification result for the limiting shapes that explain the visually remarkable properties of these Gauss paths. |
| title | The shape of quadratic Gauss paths |
| topic | Number Theory Probability 11L05 Primary, 11L40, 11N64, 60F17, 60G17, 60G50 Secondary |
| url | https://arxiv.org/abs/2508.21707 |