Sign changes in Fourier coefficients of the symmetric power $L$-functions on sums of two squares
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917931991957504 |
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| author | Kaur, Amrinder |
| author_facet | Kaur, Amrinder |
| contents | Let $f$ be a normalized primitive Hecke eigen cusp form of even integral weight $k$ for the full modular group $SL(2,\mathbb{Z})$. For integers $j \geq 2$, let $λ_{sym^j f}(m)$ denote the $m$th Fourier coefficient of the $j$th symmetric power $L$-function associated with $f$. We give a quantitative result on the number of sign changes of $λ_{sym^j f}(m)$ for the indices $m$ that are the sum of two squares in the interval $[1,x]$ for sufficiently large $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sign changes in Fourier coefficients of the symmetric power $L$-functions on sums of two squares Kaur, Amrinder Number Theory 11F11, 11F30, 11F41, 11N37 Let $f$ be a normalized primitive Hecke eigen cusp form of even integral weight $k$ for the full modular group $SL(2,\mathbb{Z})$. For integers $j \geq 2$, let $λ_{sym^j f}(m)$ denote the $m$th Fourier coefficient of the $j$th symmetric power $L$-function associated with $f$. We give a quantitative result on the number of sign changes of $λ_{sym^j f}(m)$ for the indices $m$ that are the sum of two squares in the interval $[1,x]$ for sufficiently large $x$. |
| title | Sign changes in Fourier coefficients of the symmetric power $L$-functions on sums of two squares |
| topic | Number Theory 11F11, 11F30, 11F41, 11N37 |
| url | https://arxiv.org/abs/2502.15207 |