Class of partial zeta-functions and universality

One video ‘Kacinskaite’ (42 min., 38 MB)The universality property in the Voronin sense of the Riemann zeta-function ζ(s), s = σ + it, says roughly that any analytic non-vanishing function can be approximated uniformly on any compact subsets of the strip {s ∈ C : 1/2 < σ < 1} by shifts of ζ(s). The mixed joint universality gives the possibility to connect into one tuple two different types of zeta-functions (one of those zetafunctions has the Euler product expression over primes and the other does not) and to show that any two target functions can be approximated simultaneously by a suitable vertical shift of two different type zeta- or L-functions, and that the set of such shifts has a positive lower density. In this talk, we present the mixed joint discrete universality results for the tuple consisting of the partial Matsumoto zeta-functions ϕh(s) and the periodic Hurwitz zeta-functions ζ(s, α; B), and give certain generalizationsMatematikos ir statistikos katedraVytauto Didžiojo universiteta