| Abstract [eng] |
The master‘s graduating work has been written by analyzing and presenting the joint universality theorem of Dirichlet L-functions. The work comprise 4 parts. A description of the available data has been made and the main purpose to prove the theorem has been formulated in the first part. The joint limit theorem (P_T converges weakly to P_L_ as T→∞) have been described and proved in the second part. The support of the limit measures P_L_ has been analyzed in the third part. Finally, by using some of the obtained results and a couple of auxiliary lemmas, the main result of this master’s graduating work has been proved, which is the assertion: suppose that χ_1,..., χ_r are pairwise non-equivalent Dirichlet characters. For all j=1,…,r, let K_j ⊂D be a compact subset with connected complement, and f_j (s) be a continuous non-vanishing functions on K_j which is analytic in the interior of K_j. Then, for every ε>0,we have an inequality which means, that the shifts of Dirichlet L-functions approximating the collection of given analytic function, the set is quite rich and it has a positive lover density. |
