We study the values taken by the Riemann zeta-function ζ on discrete sets. We show that infinite vertical arithmetic progressions are uniquely determined by the values of ζ taken on this set. Moreover, we prove a joint discrete universality theorem for ζ with respect to certain permutations of the set of positive integers. Finally, we study a generalization of the classical denseness theorems for ζ.
|Title of host publication
|Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto's 60th birthday
|Number of pages
|Published - 2020
|Advanced Studies in Pure Mathematics