Voronoi summation formulae and multiplicative functions on permutations

We prove a Tauberian theorem for the Voronoi summation method of divergent series with an estimate of the remainder term. The results on the Voronoi summability are then applied to analyze the mean values of multiplicative functions on random permutations.

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Bibliographic Details
Published inThe Ramanujan journal Vol. 24; no. 3; pp. 289 - 329
Main Author Zacharovas, Vytas
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.04.2011
Subjects
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
20P05
60C05
Additive functions
Multiplicative functions
40G05
Divergent series
Random permutations
Nörlund summability
Tauberian theorems
Voronoi summability
Symmetric group
Berry–Esseen bound
40E05
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Summary:We prove a Tauberian theorem for the Voronoi summation method of divergent series with an estimate of the remainder term. The results on the Voronoi summability are then applied to analyze the mean values of multiplicative functions on random permutations.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-010-9263-0