Bilinear forms with trace functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918382698233856 |
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| author | Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe Sawin, Will |
| author_facet | Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe Sawin, Will |
| contents | We obtain non-trivial bounds for bilinear sums of trace functions below the Pólya-Vinogradov range assuming only that the geometric monodromy group of the underlying ell-adic sheaf satisfies certain simple structural properties, in contrast to previous works which handled only special cases of Kloosterman and hypergeometric sheaves. Our approach builds on a general "soft" stratification theorem for sums of products of trace functions, based on an idea of Junyan Xu, combined with a new robust version of the Goursat-Kolchin-Ribet criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear forms with trace functions Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe Sawin, Will Number Theory 11T23, 11L05, 11Mxx, 11N37, 11N75, 11F66, 14F20, 14D05 We obtain non-trivial bounds for bilinear sums of trace functions below the Pólya-Vinogradov range assuming only that the geometric monodromy group of the underlying ell-adic sheaf satisfies certain simple structural properties, in contrast to previous works which handled only special cases of Kloosterman and hypergeometric sheaves. Our approach builds on a general "soft" stratification theorem for sums of products of trace functions, based on an idea of Junyan Xu, combined with a new robust version of the Goursat-Kolchin-Ribet criterion. |
| title | Bilinear forms with trace functions |
| topic | Number Theory 11T23, 11L05, 11Mxx, 11N37, 11N75, 11F66, 14F20, 14D05 |
| url | https://arxiv.org/abs/2511.09459 |