Variations of Lehmer's Conjecture for Ramanujan's tau-function

Jennifer S. Balakrishnan, William Craig, Ken Ono

We consider natural variants of Lehmer's unresolved conjecture that Ramanujan's tau-function never vanishes. Namely, for $n>1$ we prove that $$τ(n)\not \in \{\pm 1, \pm 3, \pm 5, \…