Estimates for Weyl sums in the theory of discrete universality (Q2117550)

The aim of the paper is to prove joint and disjoint discrete universality theorems for Dirichlet \(L\)-functions \(L(s, \chi)\) and Hurwitz zeta functions \(\zeta(s;\beta)\) for \(\beta \in (0,1] \cap \mathbb{Q}\) with respect to polynomials. For this purpose, the author introduces a novel approach which does not use Gallagher's lemma and it is based only on Euler product representations and zero-density estimates of \(L\)-functions, as well as mean-value estimates for Weyl sums.