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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An Abel-Tauber theorem for partitions


Author: J. L. Geluk
Journal: Proc. Amer. Math. Soc. 82 (1981), 571-575
MSC: Primary 10J20; Secondary 26A12, 40E05
MathSciNet review: 614880
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Abstract: Suppose $ \Lambda = \{ {\lambda _1},{\lambda _2}, \ldots \} $ is a given set of real numbers such that $ 0 < {\lambda _1} < {\lambda _2} < \ldots .{\text{Let }}n(u) = {\sum _{{\lambda _k} \leqslant u}}1$ and $ P(u)$ the number of solutions of $ {n_1}{\lambda _1} + {n_2}{\lambda _2} + \ldots \leqslant u$ in integers $ {n_i} \geqslant 0$. An Abel-Tauber theorem concerning $ n(u)$ and log $ P(u)$ is proved for the case where $ n(tx)/n(t) \to 1(t \to \infty )$ for $ x > 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0614880-6
PII: S 0002-9939(1981)0614880-6
Keywords: Abel-Tauber theorems, regular variation, partition function
Article copyright: © Copyright 1981 American Mathematical Society