The irreducibility of some level 1 Hecke polynomials期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The irreducibility of some level 1 Hecke polynomials

Authors:	D W Farmer K James

Institution:	Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837 ; Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975

Abstract:	Let $T_{p,k}(x)$ be the characteristic polynomial of the Hecke operator $T_{p}$ acting on the space of level 1 cusp forms $S_{k}(1)$ . We show that $T_{p,k}(x)$ is irreducible and has full Galois group over $\mathbf{Q}$ for $k\le 2000$ and , prime.

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