Short Exponential Sums and Ternary Correlations of Multiplicative Functions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915939175366656 |
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| author | Kim, Jiseong |
| author_facet | Kim, Jiseong |
| contents | In this paper, we investigate the average behavior of ternary correlations for general $k$-divisor-bounded multiplicative functions, assuming certain second moment integral bounds for the associated $L$-functions. Our approach differs from previous methods based on spectral theory or Heath-Brown-type decompositions, and instead combines the circle method with weighted short exponential-sum bounds. The key input is short exponential-sum estimates obtained from integral moment bounds for $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23250 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Short Exponential Sums and Ternary Correlations of Multiplicative Functions Kim, Jiseong Number Theory 11N37, 11L07, 11P55 In this paper, we investigate the average behavior of ternary correlations for general $k$-divisor-bounded multiplicative functions, assuming certain second moment integral bounds for the associated $L$-functions. Our approach differs from previous methods based on spectral theory or Heath-Brown-type decompositions, and instead combines the circle method with weighted short exponential-sum bounds. The key input is short exponential-sum estimates obtained from integral moment bounds for $L$-functions. |
| title | Short Exponential Sums and Ternary Correlations of Multiplicative Functions |
| topic | Number Theory 11N37, 11L07, 11P55 |
| url | https://arxiv.org/abs/2603.23250 |