On joint discrete universality of the Riemann zeta-function in short intervals - Chakraborty, Kalyan; Kanemitsu, Shigeru; Laurinčikas, Antanas (Mathematical Modelling and Analysis, 2023)
In the paper, we prove that the set of discrete shifts of the Riemann zeta-function approximating analytic nonvanishing functions f1(s),...,fr(s) defined on has a positive density in the interval [N,N + M] with with real algebraic numbers a1,...,ar linearly independent over Q. A similar result is obtained for shifts of certain absolutely convergent Dirichlet series.