Moments of random multiplicative functions over function fields
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916994007171072 |
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| author | Hofmann, Maximilian C. E. Hoganson, Annemily Menon, Siddarth Verreault, William Zaman, Asif |
| author_facet | Hofmann, Maximilian C. E. Hoganson, Annemily Menon, Siddarth Verreault, William Zaman, Asif |
| contents | Granville-Soundararajan, Harper-Nikeghbali-Radziwill, and Heap-Lindqvist independently established an asymptotic for the even natural moments of partial sums of random multiplicative functions defined over integers. Building on these works, we study the even natural moments of partial sums of Steinhaus random multiplicative functions defined over function fields. Using a combination of analytic arguments and combinatorial arguments, we obtain asymptotic expressions for all the even natural moments in the large field limit and large degree limit, as well as an exact expression for the fourth moment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08309 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moments of random multiplicative functions over function fields Hofmann, Maximilian C. E. Hoganson, Annemily Menon, Siddarth Verreault, William Zaman, Asif Number Theory Probability Granville-Soundararajan, Harper-Nikeghbali-Radziwill, and Heap-Lindqvist independently established an asymptotic for the even natural moments of partial sums of random multiplicative functions defined over integers. Building on these works, we study the even natural moments of partial sums of Steinhaus random multiplicative functions defined over function fields. Using a combination of analytic arguments and combinatorial arguments, we obtain asymptotic expressions for all the even natural moments in the large field limit and large degree limit, as well as an exact expression for the fourth moment. |
| title | Moments of random multiplicative functions over function fields |
| topic | Number Theory Probability |
| url | https://arxiv.org/abs/2408.08309 |