Israel Journal of Mathematics

, Volume 144, Issue 2, pp 343–365 | Cite as

Dirichlet series whose partial sums of coefficients have regular variation



We study pairs of Dirichlet series\(A(s) = \sum {_{n = 1}^\infty a(n)n^{ - s} } \) and\(P(s) = \sum {_{n = 2}^\infty p(n)n^{ - s} } \) in whicha(n) counts the number of objects of “size”n of some class of objects which is closed under formation of direct products and extraction of irreducible factors, andp(n) counts the number of objects of “size”n which are irreducible in this class. We prove Dirichlet series analogues of certain results about power series and use these results to prove some conjectures of Burris concerning first-order 0–1 laws.


Power Series Group Theory Direct Product Dirichlet Series Regular Variation 


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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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