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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.06087 |
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| _version_ | 1866910331546107904 |
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| author | Sharma, Prahlad |
| author_facet | Sharma, Prahlad |
| contents | We obtain the exponent of distribution $1/2+1/30$ for the ternary divisor function $d_3$ to square-free and prime power moduli, improving the previous results of Fouvry--Kowalski--Michel, Heath-Brown, and Friedlander--Iwaniec. The key input is certain estimates on bilinear sums with $GL(2)$ coefficients obtained using the delta symbol approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06087 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bilinear sums with $GL(2)$ coefficients and the exponent of distribution of $d_3$ Sharma, Prahlad Number Theory We obtain the exponent of distribution $1/2+1/30$ for the ternary divisor function $d_3$ to square-free and prime power moduli, improving the previous results of Fouvry--Kowalski--Michel, Heath-Brown, and Friedlander--Iwaniec. The key input is certain estimates on bilinear sums with $GL(2)$ coefficients obtained using the delta symbol approach. |
| title | Bilinear sums with $GL(2)$ coefficients and the exponent of distribution of $d_3$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2303.06087 |