On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912613423644672 |
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| author | Kim, Jiseong |
| author_facet | Kim, Jiseong |
| contents | In this paper, we study the average of shifted sum for general multiplicative functions. As applications, we prove non-trivial upper bounds for weighted averages of shifted convolutions involving $GL(2)$ and $GL(3)$ Fourier coefficients without smoothing. We apply square-root cancellation on average over short intervals for $GL(2)$ Fourier coefficients with the standard Hardy-Littlewood circle method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients Kim, Jiseong Number Theory 11F30, 11P55 In this paper, we study the average of shifted sum for general multiplicative functions. As applications, we prove non-trivial upper bounds for weighted averages of shifted convolutions involving $GL(2)$ and $GL(3)$ Fourier coefficients without smoothing. We apply square-root cancellation on average over short intervals for $GL(2)$ Fourier coefficients with the standard Hardy-Littlewood circle method. |
| title | On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients |
| topic | Number Theory 11F30, 11P55 |
| url | https://arxiv.org/abs/2509.24152 |