| Abstract [eng] |
The Lerch zeta-functionL(λ,α,s),s=σ+it, depends on two realparametersλand 0< α⩽1, and, forσ >1, is defined by the Dirichlet seriesP∞m=0e2πiλm(m+α)−s, and by analytic continuation elsewhere. In the paper, weconsider the joint approximation of collections of analytic functions by discrete shifts(L(λ1,α1,s+ikh1),...,L(λr,αr,s+ikhr)),k= 0,1,..., with arbitraryλj, 0< αj⩽1 andhj>0,j= 1,...,r. We prove that there exists a non-empty closed set ofanalytic functions on the critical strip 1/2< σ <1 which is approximated by theabove shifts. It is proved that the set of shifts approximating a given collection ofanalytic functions has a positive lower density. The case of positive density also isdiscussed. A generalization for some compositions is given. |
