| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4594876 | Journal of Number Theory | 2009 | 6 Pages |
Abstract
It is a classical result that the number of primes ℓ for which τ(ℓ) vanishes has Dirichlet density 0, where τ(ℓ) is the Ramanujan τ function. We study an analogous question that arises in studying the Λ-adic representation whose image is full. In particular, we show that the set of primes ℓ for which the trace of the Frobenius at ℓ has positive μ-invariant has Dirichlet density 0. We also discuss the analogous Dirichlet densities related to λ-invariants.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
