What the slopes are

Let \(f\) be a classical modular eigenform of weight \(k\), for example, \(f = \Delta\). The Ramanujan conjecture states that the Hecke eigenvalues \(a_p\) satisfy the bound \(|a_p| \le 2 p^{(k-1)/2}.\) A slightly fancier but cleaner way of saying this … Continue reading →