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Discrete limit theorems for general Dirichlet series. III

A. Laurinčikas, R. Macaitienė (2004)

Open Mathematics

Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.

Discrete limit theorems for the Laplace transform of the Riemann zeta-function

Roma Kačinskaitė, Antanas Laurinčikas (2005)

Acta Mathematica Universitatis Ostraviensis

In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.

Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ -function

Nikolai Nikolski (1995)

Annales de l'institut Fourier

It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plan free of zeros of the Riemann ζ -function.

Distribution of values of Hecke characters of infinite order

C. S. Rajan (1998)

Acta Arithmetica

We show that the number of primes of a number field K of norm at most x, at which the local component of an idele class character of infinite order is principal, is bounded by O(x exp(-c√(log x))) as x → ∞, for some absolute constant c > 0 depending only on K.

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