Analytic and asymptotic properties of Linnik's probability densities

Date

1994

Authors

Hayfavi, A.
Kotz, S.
Ostrovskii, I. V.

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Abstract

The analytic and asymptotic properties of the probability density Jin (:r:) introduced in 1953 by Ju. V. Linnik and defined by the characteristic function 1/(1 + It I"), 0 < n < 2, are studied. Expansions of Jin (:r:) into convergent and asymptotic series in terms of log I :r: I , I x I k n, I ,r I k (k = 0, 1, 2, ... ) are obtained. It turns out that the analytic structure of Pc, (:r:) depends substantially on the arithmetical nature of the parameter n.

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Comptes Rendus de l'Académie des Sciences - Series I - Mathematics

Publisher

Elsevier

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Published Version (Please cite this version)

Language

English
French