On the distribution of the Fourier coefficients over two sparse sequences
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915751721435136 |
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| author | Venkatasubbareddy, Kampamolla |
| author_facet | Venkatasubbareddy, Kampamolla |
| contents | Let $j\geq 3$ be any fixed integer and $f$ be a primitive holomorphic cusp form of even integral weight $κ\geq 2$ for the full modular group $SL(2,\mathbb{Z})$. We write $λ_{{\rm{sym}^j }f}(n)$ for the $n^\text{th}$ normalized Fourier coefficient of $L(s,{\rm{sym}}^j f)$. In this article, we establish asymptotic formulae for the discrete sums of the Fourier coefficients $λ_{\rm{sym}^j f}^2(n)$ over two sparse sequence of integers, which can be written as the sum of four integral squares and the sum of six integral squares, with refined error terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the distribution of the Fourier coefficients over two sparse sequences Venkatasubbareddy, Kampamolla Number Theory Let $j\geq 3$ be any fixed integer and $f$ be a primitive holomorphic cusp form of even integral weight $κ\geq 2$ for the full modular group $SL(2,\mathbb{Z})$. We write $λ_{{\rm{sym}^j }f}(n)$ for the $n^\text{th}$ normalized Fourier coefficient of $L(s,{\rm{sym}}^j f)$. In this article, we establish asymptotic formulae for the discrete sums of the Fourier coefficients $λ_{\rm{sym}^j f}^2(n)$ over two sparse sequence of integers, which can be written as the sum of four integral squares and the sum of six integral squares, with refined error terms. |
| title | On the distribution of the Fourier coefficients over two sparse sequences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.07037 |