On Shimura's decomposition
| Autor: | Purkait, Soma |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | International Journal of Number Theory Vol. 9, No. 6 (2013) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S179304211350036X |
| Popis: | Let $k$ be an odd integer $\ge 3$ and $N$ a positive integer such that $4 \mid N$. Let $\chi$ be an even Dirichlet character modulo $N$. Shimura decomposes the space of half-integral weight cusp forms $S_{k/2}(N,\chi)$ as a direct sum of $S_0(N,\chi)$ (the subspace spanned by 1-variable theta- series) and $S_{k/2}(N,\chi,\phi)$ where $\phi$ runs through a certain family of integral weight newforms. The explicit computation of this decomposition is important for practical applications of a theorem of Waldspurger relating critical values of $L$-functions of quadratic twists of newforms of even weight to coefficients of modular forms of half-integral weight. Comment: 12 pages, to appear in the International Journal of Number Theory |
| Databáze: | arXiv |
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