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 | References | Similar Articles | Additional Information

Let be the characteristic polynomial of the Hecke operator acting on the space of level 1 cusp forms . We show that is irreducible and has full Galois group over for and , prime.

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Additional Information

**D. W. Farmer**

Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837

Email:
farmer@bucknell.edu

**K. James**

Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975

Email:
kevja@clemson.edu

DOI:
https://doi.org/10.1090/S0025-5718-01-01375-8

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