Titlebook: Limit Theorems for the Riemann Zeta-Function; Antanas Laurinčikas Book 1996 Springer Science+Business Media Dordrecht 1996 Rang.number the

上下倒置

Mathematics and Its Applicationshttp://image.papertrans.cn/l/image/586171.jpg

古代

时代

密码

Limit Theorems for the Riemann Zeta-Function on the Complex Plane,Since the function .(.) is complex-valued the distribution of its values is reflected more adequately by limit theorems on the complex plane C. In this chapter we will obtain such theorems on the half-plane . ≥ 1/2.

START

Limit Theorems for the Riemann Zeta-Function in the Space of Analytic Functions,Let .. = {. ∈ .: 1/2 < . < 1} and .. = {. ∈ .: . > 1}. We define the probability measures . on (.(..), .(.(..))), . = 1, 2. The aim of this chapter is to prove that the measures .., converge weakly to some measure as . → ∞. Let . = {. ∈ .: . > 1/2}.

radiograph

Universality Theorem for the Riemann Zeta-Function,In this chapter we apply the limit theorem for the Riemann zeta-function in the space .(..) to obtain one of magnificent properties of this function — the universality property. Roughly speaking, this property asserts that any analytic function can be approximated uniformly on compact subsets of .. by translations of ζ(.).

somnambulism

fender

Limit Theorems for Dirichlet ,-Functions,The properties of Dirichlet .-functions with a fixed modulus are similar to those of the Riemann zeta-function. Therefore all limit theorems proved in the previous chapter can be stated also for Dirichlet .-functions. In this chapter we will give only few limit theorems which describe the asymptotic behaviour of the Dirichlet .-functions.

FLIRT

978-90-481-4647-5Springer Science+Business Media Dordrecht 1996

Hyperopia

Elements of the Probability Theory,ying of the distribution of values of some functions defined by the Dirichlet series. Most of the material consists of well-known facts, and their proofs can be found in monographs on the theory of probability.