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A note on the dimension of the largest Hecke submodule. (arXiv:1810.02006v1 [math.NT])
来源于:arXiv
For $k\ge 2$ even, let $d_{k,N}$ denote the dimension of the largest simple
Hecke submodule of $S_{k}(\Gamma_0(N); \mathbb{Q})$. We show, using a simple
analytic method, that $d_{k,N} \gg_k \log\log N / \log(2p)$ with $p$ the
smallest prime co-prime to $N$. Previously, bounds of this quality were only
known for prime $N \equiv 7 \pmod{8}$ and $k=2$, using an algebraic method
based on congruences. We also establish similar (and sometimes stronger)
results concerning $S_{k}(\Gamma_0(N), \chi)$, with $k \geq 2$ an integer and
$\chi$ an arbitrary nebentypus. 查看全文>>