Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11F11

Retrieve articles in all journals with MSC (2000): 11F11


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: http://dx.doi.org/10.1090/S0025-5718-01-01375-8
PII: S 0025-5718(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