Triple Correlation Sums of Coefficients of Cusp Forms
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866909704035237888 |
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| author | Hulse, Thomas A. Kuan, Chan Ieong Lowry-Duda, David Walker, Alexander |
| author_facet | Hulse, Thomas A. Kuan, Chan Ieong Lowry-Duda, David Walker, Alexander |
| contents | We produce nontrivial asymptotic estimates for shifted sums of the form $\sum a(h)b(m)c(2m-h)$, in which $a(n),b(n),c(n)$ are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate how to strengthen them under the Riemann Hypothesis. As an application, we show that there are infinitely many three term arithmetic progressions $n-h, n, n+h$ such that $a(n-h)a(n)a(n+h) \neq 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_09216 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Triple Correlation Sums of Coefficients of Cusp Forms Hulse, Thomas A. Kuan, Chan Ieong Lowry-Duda, David Walker, Alexander Number Theory 11F11, 11M32 We produce nontrivial asymptotic estimates for shifted sums of the form $\sum a(h)b(m)c(2m-h)$, in which $a(n),b(n),c(n)$ are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate how to strengthen them under the Riemann Hypothesis. As an application, we show that there are infinitely many three term arithmetic progressions $n-h, n, n+h$ such that $a(n-h)a(n)a(n+h) \neq 0$. |
| title | Triple Correlation Sums of Coefficients of Cusp Forms |
| topic | Number Theory 11F11, 11M32 |
| url | https://arxiv.org/abs/1911.09216 |