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A Multiplicative Analogue of Schur's Tauberian Theorem

  • Karen Yeats (a1)

Abstract

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.

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References

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[1] Apostol, Tom M., Introduction to Analytic Number Theory. Springer-Verlag, New York, 1976.
[2] Bender, Edward A., Asymptotic methods in enumeration. SIAM Rev. 16 (1974), 485515.
[3] Bingham, N. H., Goldie, C. M. and Teugels, J. L., Regular Variation. Cambridge University Press, Cambridge, 1987.
[4] Burris, Stanley N., Number Theoretic Density and Logical Limit Laws. Math. Surveys Monogr. 86, Amer.Math. Soc., Providence, RI, 2001.
[5] Geluk, J. L. and de Haan, L., Regular variation, extensions and Tauberian theorems. Centrum voor Wiskunde en Informatica, Amsterdam, 1987.
[6] Hardy, G. H. and Riesz, Marcel. The General Theory of Dirichlet's Series. Cambridge University Press, Cambridge, 1952.
[7] Knopfmacher, John, Abstract Analytic Number Theory. North-Holland Mathematical Library 12, North-Holland, Amsterdam, 1975; Available as a Dover Reprint.
[8] Odlyzko, A. M., Asymptotic enumeration methods. Handbook of Combinatorics 12, 10631229, Elsevier, Amsterdam, 1995.
[9] Pólya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis. I. Springer-Verlag, Berlin, 1970.
[10] Schur, I., Problem:. Arch. Math. Phys. Ser. 3 27(1918), 162.
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A Multiplicative Analogue of Schur's Tauberian Theorem

  • Karen Yeats (a1)

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