ANALYTIC AND ASYMPTOTIC PROPERTIES OF LINNIKS PROBABILITY DENSITIES

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1994-11-03

Author

HAYFAVI, A
KOTZ, S
OSTROVSKII, IV

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

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https://hdl.handle.net/11511/66865

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COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE

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Department of Mathematics, Article

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Citation Formats

A. HAYFAVI, S. KOTZ, and I. OSTROVSKII, “ANALYTIC AND ASYMPTOTIC PROPERTIES OF LINNIKS PROBABILITY DENSITIES,” COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, pp. 985–990, 1994, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66865.