ADDITIVE PROBLEMS OF DIVISORS

The work covers the additive properties of multiplicative functions. The aim is to deduce the asymptotic formulae for a number of the integer representation in the Diophantine equations and to construct the theory for evaluating sums of the Dirichlet characters. The theory of algebraic numbers, variants of circular method and also the methods for evaluations of the trigonometric sums and Dirichlet character sums from polynomials and rational functions have been applied. The asymptotic formulae for number of the integer representations in the Diophantine equations have been obtained, the theory for evaluating total sums of the Dirichlet characters from polynomials and rational functions has been constructed. The results can find application in the Moscow State University, in the Mathematical Insitute (Russian Academy of Sciences), in the institutes of mathematics of Tadjikistan and Uzbekistan, in the Tadjik State University. The results and methods can be applied to the solution of different problems in the analytical number theoryAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio