Viena jungtinė universalumo teorema
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 parame...
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Lithuanian Academic Libraries Network (LABT)
2014
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ndltd-LABT_ETD-oai-elaba.lt-LT-eLABa-0001-E.02~2011~D_20140701_164124-318342014-07-15T03:51:49Z2014-07-01litJanulis, KęstutisViena jungtinė universalumo teoremaOne joint universality theoremLithuanian Academic Libraries Network (LABT)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.Unversalumo teoremaDzeta funkcijaHurvico funkcijaMaster thesisLaurinčikas, AntanasVilnius UniversityVilnius Universityhttp://vddb.library.lt/obj/LT-eLABa-0001:E.02~2011~D_20140701_164124-31834LT-eLABa-0001:E.02~2011~D_20140701_164124-31834VU-nmdasecotfq-20140701-164124http://vddb.library.lt/fedora/get/LT-eLABa-0001:E.02~2011~D_20140701_164124-31834/DS.005.0.01.ETDUnrestrictedapplication/pdf |
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Lithuanian |
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Dissertation |
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Unversalumo teorema Dzeta funkcija Hurvico funkcija |
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Unversalumo teorema Dzeta funkcija Hurvico funkcija Janulis, Kęstutis Viena jungtinė universalumo teorema |
description |
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. |
author2 |
Laurinčikas, Antanas |
author_facet |
Laurinčikas, Antanas Janulis, Kęstutis |
author |
Janulis, Kęstutis |
author_sort |
Janulis, Kęstutis |
title |
Viena jungtinė universalumo teorema |
title_short |
Viena jungtinė universalumo teorema |
title_full |
Viena jungtinė universalumo teorema |
title_fullStr |
Viena jungtinė universalumo teorema |
title_full_unstemmed |
Viena jungtinė universalumo teorema |
title_sort |
viena jungtinė universalumo teorema |
publisher |
Lithuanian Academic Libraries Network (LABT) |
publishDate |
2014 |
url |
http://vddb.library.lt/fedora/get/LT-eLABa-0001:E.02~2011~D_20140701_164124-31834/DS.005.0.01.ETD |
work_keys_str_mv |
AT januliskestutis vienajungtineuniversalumoteorema AT januliskestutis onejointuniversalitytheorem |
_version_ |
1716708166171885568 |