Toy models for D. H. Lehmer's conjecture
Toy models for D. H. Lehmer's conjecture
In 1947, Lehmer conjectured that the Ramanujan $\tau$-function $\tau (m)$ never vanishes for all positive integers $m$, where $\tau (m)$ are the Fourier coefficients of the cusp form $\Delta_24$ of weight $12$. Lehmer verified the conjecture in 1947 for $m < 214928639999$. In 1973, Serre verified up to $m < …