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Mathematics of Computation

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The irreducibility of some level 1 Hecke polynomials

Authors: D. W. Farmer and K. James
Journal: Math. Comp. 71 (2002), 1263-1270
MSC (2000): Primary 11F11
Published electronically: June 22, 2001
MathSciNet review: 1898755
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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 $p<2000$, $p$ prime.

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Additional Information

D. W. Farmer
Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
MR Author ID: 341467

K. James
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975
MR Author ID: 629241

Received by editor(s): January 6, 2000
Received by editor(s) in revised form: September 4, 2000
Published electronically: June 22, 2001
Additional Notes: The research of the first author was supported in part by the American Institute of Mathematics. We thank the referee for many helpful comments
Article copyright: © Copyright 2001 American Mathematical Society