I will discuss a recent progress on two classical problems. The first one comes mostly from applied mathematics and numerical analysis: find tight universal and preferably simple enclosures for zeros of Bessel functions, of their derivatives, and possibly of other special functions. The second one comes primarily from number theory: find bounds for the number of lattice points under the graph of a given function (with some restrictions on the class of functions). As an application of these results, I’ll show the validity of inequalities à la Pólya for the magnetic Aharonov--Bohm Laplacian in the disk, discuss possible generalisations, and open problems. The talk covers some joint works, mostly in progress, with N. Filonov, I. Polterovich, and D. A. Sher.