Smooth numbers in arithmetic progressions to large moduli
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912589188956160 |
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| author | Pascadi, Alexandru |
| author_facet | Pascadi, Alexandru |
| contents | We show that smooth numbers are equidistributed in arithmetic progressions to moduli of size $x^{66/107-o(1)}$. This overcomes a longstanding barrier of $x^{3/5-o(1)}$ present in previous works of Bombieri-Friedlander-Iwaniec, Fouvry-Tenenbaum, Drappeau, and Maynard. We build on Drappeau's variation of the dispersion method and on exponential sum manipulations of Maynard, ultimately relying on optimized Deshouillers-Iwaniec type estimates for sums of Kloosterman sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11696 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Smooth numbers in arithmetic progressions to large moduli Pascadi, Alexandru Number Theory 11N25 We show that smooth numbers are equidistributed in arithmetic progressions to moduli of size $x^{66/107-o(1)}$. This overcomes a longstanding barrier of $x^{3/5-o(1)}$ present in previous works of Bombieri-Friedlander-Iwaniec, Fouvry-Tenenbaum, Drappeau, and Maynard. We build on Drappeau's variation of the dispersion method and on exponential sum manipulations of Maynard, ultimately relying on optimized Deshouillers-Iwaniec type estimates for sums of Kloosterman sums. |
| title | Smooth numbers in arithmetic progressions to large moduli |
| topic | Number Theory 11N25 |
| url | https://arxiv.org/abs/2304.11696 |