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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.

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