| Abstract [eng] |
Let L(s,χ),s=σ+it, denote the Dirichlet L – function, and ζ(s,α) be the Hurwitz zeta-function with parameter α,0<α≤1. We prove the following statment. Suppose that the number α is transcendental, and K_1 and K_2 are compact subsets of strip D={ s∊ C: 1/2<σ<1} with connected complements. Let f_1 (s) be a continuous non-vanishing function on K_1 which is analytic in the interior of K_1, and f_2 (s) be a continuous function on K_2, and analytic in the interior of K_2. Then, for every ε>0, liminf┬(T→∞)⁡〖1/T meas{τ∊[0;T]: 〖sup〗┬(s∊K_1 )⁡〖|L(s+iτ,χ)-f_1 (s) |<ε〗, sup┬(s∊K_2 )⁡〖|ζ(s+iτ,α)-f_2 (s) |<ε〗}〗>0. There meas{A} denotes the Lebesgue measure of a measurable set A⊂R. |
