Abstract
Let T n,k (X) be the characteristic polynomial of the nth Hecke operator acting on the space of cusp forms of weight k for the full modular group. We record a simple criterion which can be used to check the irreducibility of the polynomials T n,k (X). Using this criterion with some machine computation, we show that if there exists n ≥ 2 such that T n,k (X) is irreducible and has the full symmetric group as Galois group, then the same is true of T p,k (X) for each prime p < 4,000,000.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
