After the proof by R. Apéry of the irrationality of ζ(3) in 1976, a number of articles have been devoted to the study of Diophantine properties of values of the Riemann zeta function at positive integers. A survey has been written by S. Fischler for the Bourbaki Seminar in November 2002 [6]. Here, we review more recent results, including contributions by P. Bundschuh, S. Bruiltet, C. Elsner, S....

We prove the second order vanishing of a new family of character combinations of Hurwitz zeta functions, thus answering a query of Anderson in [And02]. Along the way, we prove a family of new trigonometric identities.

We give a new type of mixed discrete joint universality properties, which is satisfied by wide class zeta-functions. study the for certain modification Matsumoto zeta-functions $\varphi_h(s)$ and collection periodic Hurwitz $\zeta(s,\alpha;\mathfrak{B})$ under condition that common difference arithmetical progression $h \gt 0$ such $\exp \big\{ \frac{2\pi}{h} \big\}$ rational number parameter $...

In this thesis we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet’s L-function. We have also investigated some fundamental concepts related to these functions and their universality properties. In addition, we ...