Magistro darbo tikslas yra įrodyti Mišu teoremos analogą funkcijoms L(s,χ) ir ζ(s,α) su transcendenčiuoju parametru α. / 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.
| Identifer | oai:union.ndltd.org:LABT_ETD/oai:elaba.lt:LT-eLABa-0001:E.02~2011~D_20140701_164124-31834 |
| Date | 01 July 2014 |
| Creators | Janulis, Kęstutis |
| Contributors | Laurinčikas, Antanas, Vilnius University |
| Publisher | Lithuanian Academic Libraries Network (LABT), Vilnius University |
| Source Sets | Lithuanian ETD submission system |
| Language | Lithuanian |
| Detected Language | English |
| Type | Master thesis |
| Format | application/pdf |
| Source | http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2011~D_20140701_164124-31834 |
| Rights | Unrestricted |
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