Dirichlet L-function

Abstract: Preface 1 Elements of the probability theory 2 Dirichlet series and Dirichlet polynomials 3 Limit theorems for the modulus of the Riemann Zeta-function 4 Limit theorems for the Riemann Zeta-function on the complex plane 5 Limit theorems for the Riemann Zeta-function in the space of analytic functions 6 Universality theorem for the Riemann Zeta-function 7 Limit theorem for the Riemann Zeta-function in the space of continuous functions 8 Limit theorems for Dirichlet L-functions 9 Limit theorem for the Dirichlet series with multiplicative coefficients References Notation Subject index

Abstract: in domains f~ in Euclidean n-space, R n, where f is a given symmetric function on R n, A denotes the eigenvalues A1, ..., An of the Hessian matrix of second derivatives D2u and r is a given function in f t • n. Equations of this type were treated by Calfarelli, Nirenberg and Spruek [2], for the case r 1 6 2 who demonstrated the existence of classical solutions for the Dirichiet problem, under various hypotheses on the function f and the domain ft. Their results extended their previous work [1], and that of Krylov [13], Ivochkina [8] and others, on equations of Monge-Amp~re type,