Geodesic
A Multiplicative Analogue of Schur's Tauberian Theorem
Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 473-480

Voir la notice de l'article provenant de la source Cambridge University Press

A theorem concerning the asymptotic behaviour of partial sums of the coefficients of products of Dirichlet series is proved using properties of regularly varying functions. This theorem is a multiplicative analogue of Schur's Tauberian theorem for power series.
DOI : 10.4153/CMB-2003-046-5
Mots-clés : 11N45 
Yeats, Karen. A Multiplicative Analogue of Schur's Tauberian Theorem. Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 473-480. doi: 10.4153/CMB-2003-046-5
@article{10_4153_CMB_2003_046_5,
     author = {Yeats, Karen},
     title = {A {Multiplicative} {Analogue} of {Schur's} {Tauberian} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {473--480},
     year = {2003},
     volume = {46},
     number = {3},
     doi = {10.4153/CMB-2003-046-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-046-5/}
}
TY  - JOUR
AU  - Yeats, Karen
TI  - A Multiplicative Analogue of Schur's Tauberian Theorem
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 473
EP  - 480
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-046-5/
DO  - 10.4153/CMB-2003-046-5
ID  - 10_4153_CMB_2003_046_5
ER  - 
%0 Journal Article
%A Yeats, Karen
%T A Multiplicative Analogue of Schur's Tauberian Theorem
%J Canadian mathematical bulletin
%D 2003
%P 473-480
%V 46
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-046-5/
%R 10.4153/CMB-2003-046-5
%F 10_4153_CMB_2003_046_5

[1] [1] Apostol, Tom M., Introduction to Analytic Number Theory. Springer-Verlag, New York, 1976. Google Scholar

[2] [2] Bender, Edward A., Asymptotic methods in enumeration. SIAM Rev. 16 (1974), 485–515. Google Scholar

[3] [3] Bingham, N. H., Goldie, C. M. and Teugels, J. L., Regular Variation. Cambridge University Press, Cambridge, 1987. Google Scholar

[4] [4] Burris, Stanley N., Number Theoretic Density and Logical Limit Laws. Math. Surveys Monogr. 86, Amer.Math. Soc., Providence, RI, 2001. Google Scholar

[5] [5] Geluk, J. L. and de Haan, L., Regular variation, extensions and Tauberian theorems. Centrum voor Wiskunde en Informatica, Amsterdam, 1987. Google Scholar

[6] [6] Hardy, G. H. and Riesz, Marcel. The General Theory of Dirichlet's Series. Cambridge University Press, Cambridge, 1952. Google Scholar

[7] [7] Knopfmacher, John, Abstract Analytic Number Theory. North-Holland Mathematical Library 12, North-Holland, Amsterdam, 1975; Available as a Dover Reprint. Google Scholar

[8] [8] Odlyzko, A. M., Asymptotic enumeration methods. Handbook of Combinatorics 1–2, 1063–1229, Elsevier, Amsterdam, 1995. Google Scholar

[9] [9] Pólya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis. I. Springer-Verlag, Berlin, 1970. Google Scholar

[10] [10] Schur, I., Problem:. Arch. Math. Phys. Ser. 3 27(1918), 162. Google Scholar

Cité par Sources :