Exponential sums over integers without large prime divisors
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915271702216704 |
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| author | Drappeau, Sary Shparlinski, Igor E. |
| author_facet | Drappeau, Sary Shparlinski, Igor E. |
| contents | We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $ν\ne 0$, we also obtain new bounds on exponential sums with $ν$-th powers of such integers. The improvement is based on exploiting more precisely the factorisation of integers without large prime divisors, along with existing Type~I and Type~II bounds. For $ν=1$ we use the classical bounds of Vinogradov (1937), while for $ν\neq 1$ we use bounds of Vaughan (1975) as well as of Fouvry, Kowalski and Michel (2014). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential sums over integers without large prime divisors Drappeau, Sary Shparlinski, Igor E. Number Theory We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $ν\ne 0$, we also obtain new bounds on exponential sums with $ν$-th powers of such integers. The improvement is based on exploiting more precisely the factorisation of integers without large prime divisors, along with existing Type~I and Type~II bounds. For $ν=1$ we use the classical bounds of Vinogradov (1937), while for $ν\neq 1$ we use bounds of Vaughan (1975) as well as of Fouvry, Kowalski and Michel (2014). |
| title | Exponential sums over integers without large prime divisors |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.10278 |