On Signs of eigenvalues of Modular forms satisfying Ramanujan Conjecture
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913609869688832 |
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| author | Addanki, Nagarjuna Chary |
| author_facet | Addanki, Nagarjuna Chary |
| contents | Let $F \in S_{k_1}(Γ^{(2)}(N_1))$ and $G \in S_{k_2}(Γ^{(2)}(N_2))$ be two Siegel cusp forms over the congruence subgroups $Γ^{(2)}(N_1)$ and $Γ^{(2)}(N_2)$ respectively. Assume that they are Hecke eigenforms in different eigenspaces and satisfy the Generalized Ramanujan Conjecture. Let $λ_F(p)$ denote the eigenvalue of $F$ with respect to the Hecke operator $T(p)$. In this article, we compute a lower bound for the density of the set of primes, $\{ p : λ_F(p) λ_G(p) < 0 \}.$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_09738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Signs of eigenvalues of Modular forms satisfying Ramanujan Conjecture Addanki, Nagarjuna Chary Number Theory Let $F \in S_{k_1}(Γ^{(2)}(N_1))$ and $G \in S_{k_2}(Γ^{(2)}(N_2))$ be two Siegel cusp forms over the congruence subgroups $Γ^{(2)}(N_1)$ and $Γ^{(2)}(N_2)$ respectively. Assume that they are Hecke eigenforms in different eigenspaces and satisfy the Generalized Ramanujan Conjecture. Let $λ_F(p)$ denote the eigenvalue of $F$ with respect to the Hecke operator $T(p)$. In this article, we compute a lower bound for the density of the set of primes, $\{ p : λ_F(p) λ_G(p) < 0 \}.$ |
| title | On Signs of eigenvalues of Modular forms satisfying Ramanujan Conjecture |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.09738 |