TY - CHAP
T1 - The values of the Riemann zeta-function on discrete sets
AU - Lee, Junghun
AU - Sourmelidis, Athanasios
AU - Steuding, Jörn
AU - Suriajaya, Ade Irma
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://dx.doi.org/10.2969/aspm/08410315
U2 - 10.2969/aspm/08410315
DO - 10.2969/aspm/08410315
M3 - Chapter
SN - 9784864970891
SN - 9784864970884
T3 - Advanced Studies in Pure Mathematics
SP - 315
EP - 334
BT - Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto's 60th birthday
ER -