Koopa Koo

University of Washington Seattle | UW · Department of Mathematics

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-i...

Let f be a non-CM newform of weight k > 1. Let L be a subfield of the coefficient field of f. We completely settle the question of the density of the set of primes p such that the p-th coefficient of f generates the field L. This density is determined by the inner twists of f. As a particular case, we obtain that in the absence of non-trivial inner...