On the minus parts of classical Poincar\'e series
Let $S_k(N)$ be the space of cusp forms of weight $k$ for $\Gamma_0(N)$. We show that $S_k(N)$ is the direct sum of subspaces $S_k^+(N)$ and $S_k^-(N)$. Where $S_k^+(N)$ is the vector space of cusp forms of weight $k$ for the group $\Gamma_0^+(N)$ generated by $\Gamma_0(N)$ and $W_N$ and $S_k^-(N)$...
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| Published in | 충청수학회지, 31(3) pp. 281 - 285 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
충청수학회
01.08.2018
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Let $S_k(N)$ be the space of cusp forms of weight $k$ for $\Gamma_0(N)$.
We show that $S_k(N)$ is the direct sum of subspaces $S_k^+(N)$ and $S_k^-(N)$. Where $S_k^+(N)$ is the vector space of cusp forms of weight $k$ for the group $\Gamma_0^+(N)$ generated by $\Gamma_0(N)$ and $W_N$ and $S_k^-(N)$ is the subspace consisting of elements $f$ in $S_k(N)$ satisfying $f|_kW_N=-f$. We find generators spanning the space $S_k^-(N)$ from Poincar\'e series and give all linear relations among such generators. KCI Citation Count: 0 |
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| ISSN: | 1226-3524 2383-6245 |
| DOI: | 10.14403/jcms.2018.31.1.281 |