4 problems

Atkin–Serre conjecture. For every $\varepsilon>0$, there exist constants $c(\varepsilon),d(\varepsilon)>0$ such that, for all primes $p>d(\varepsilon)$,

Let $\tau(n)$ be Ramanujan's tau function, the Fourier coefficients of the discriminant modular form $\Delta$, and let $p$ range over primes. Lehmer's conjecture. If $n\geq 1$, the…

Let $q=e^{2\pi i z}$, and let … be a newform, where $k\in\{12,16,18,20,22,26\}$. Lehmer's conjecture. For every such $k$ and every positive integer $n$, … For $k=12$, this is Lehme…

Let $Q$ denote the first quadrant of the complex plane, and let $\Xi_{\Delta,N}(z)$ be the truncation after $N$ terms of the hyperbolic-gamma-function series defining the Ramanujan…