Magistro darbo tikslas yra įrodyti Mišu teoremos analogą funkcijoms L(s,&#967;) ir &#950;(s,&#945;) su transcendenčiuoju parametru &#945;. / Let L(s,&#967;),s=&#963;+it, denote the Dirichlet L – function, and &#950;(s,&#945;) be the Hurwitz zeta-function with parameter &#945;,0<&#945;&#8804;1. We prove the following statment. Suppose that the number &#945; is transcendental, and K_1 and K_2 are compact subsets of strip D={ s&#8714; C: 1/2<&#963;<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 &#949;>0, liminf&#9516;(T&#8594;&#8734;)&#8289;&#12310;1/T meas{&#964;&#8714;[0;T]: &#12310;sup&#12311;&#9516;(s&#8714;K_1 )&#8289;&#12310;|L(s+i&#964;,&#967;)-f_1 (s) |<&#949;&#12311;, sup&#9516;(s&#8714;K_2 )&#8289;&#12310;|&#950;(s+i&#964;,&#945;)-f_2 (s) |<&#949;&#12311;}&#12311;>0. There meas{A} denotes the Lebesgue measure of a measurable set A&#8834;R.

B. von Bahr irode teorema, kurios rezultato optimalumas nezinomas. Sio uzdavinio sprendimui yra reikalingas asimtotinis skleidinys, esantis darbe. / B. von Bahr proved theorem which result is more useful when is shown the asymptotics of it. This asymptotics is the result of work.

In this research work it is strived to examine some of the elements of mathematics analysis such as function, derivative, line, which were published in the textbooks for the higher schools in the 4th decade in the XX th century in Lithuania. These elements were analyzed separately, examining the theory presented in the textbooks of Ketarauskas, Juška, Vaičekauskas, Šikšnys of the afore-mentioned time. It is compared with the facts, proofs, tasks and solution methods which are presented in the textbooks for secondary schools of Lithuanian authors (end of the XX th century). In such a way, not only theory, but practical tasks, illustrating the teaching material, were examined, strengthening theoretical knowledge, forming logical and critical thinking.

Tegul funkcija &#966;(s) s=&#963;+it, yra apibrėžta srityje &#963;>&#945;+&#946;+1 polinomine Oilerio sandauga. Magistro darbe įrodyta diskreti ribinė teorema analizinių funkcijų erdvėje H(D), funkcijai &#966;(s). Tarkime, kad h>0 toks fiksuotas skaičius, kad kuriems nors sveikiems k&#8800;0 skaičius exp{2&#960;k/h} yra racionalus, o B(H(D)) yra erdvės H(D) Borelio aibių klasė. Darbe įrodyta, kad tikimybinis matas silpnai konverguoja į vieno H(D) reikšmio atsitiktinio elemento skirstinį. / For &#963;>&#945;+&#946;+1, define the function &#966;(s), s=&#963;+it, by a polynomial Euler product. In our work, a discrete limit theorem in the space H(D) of analytic functions for the function &#966;(s) is proved. Suppose that h>0 is a fixed number such that for some integers k&#8800;0 the number exp{2&#960;k/h} is racional, and denote by B(H(D)) the class of Borel sets of the space H(D). Then we prove that the probability measure converges weakly to the distribution of one H(D)- valued random element.

Darbe prisimenami jau esami rezultatai ir įrodoma ribinė teorema su svoriu analizinių funkcijų erdvėje bendrosioms Dirichlė eilutėms. / Work reminds existing results and proves a weighted limit theorem in the space of analytic functions for general Dirichlet series.

Nagrinėjamos dvi funkcijos. Darbe nustatyta, kad esant papildomiems reikalavimams, šios funkcijos turi be galo daug nulių atitinkamoje juostoje ir pusplokštumoje. / The two functions are analytically continuable to the whole complex plane. It is prove that the functions have infinitely many zeros in the strop and in the half-plane.

This work outcomes with the proof that Dirichlet L-functions are correct for two-dimensional limit theorem .

Bengt von Bahr irode reorema, kurios rezultato optimalumas yra nezinomas.Sio uzdavinio sprendimui yra reikalinga pasiskirstymo funkcijos asimptotinis skleidinys esantis darbe. / Bengt von Bahr proved theorem which rezult is more useful then is shown.the asymptotics is the result of work.

Dans cet ouvrage on résout un problème de totalisation de valeurs des fonctions multiplicatives. On analyse une classe qui possède de pareilles fonctions. Cette classe contient trois conditions. La plus importante des conditions et celle des fonctions de la classe qui sont proches de l'unité dans la multitude des nombres premiers. On est montré qu’on peut améliorer le membre restant pour la fonction concrète.

Šis darbas yra apie periodinės dzeta funkcijos reikšmių sandaugos formulės radimą. / In the bachelor work, we consider the function zeta[lemda](s) with rational parameter lemda.