Binomial Sums and Functions of Exponential Type |
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Authors: | Mashreghi Javad; Ransford Thomas |
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Institution: | Département de mathématiques et de statistique, Université Laval Québec (QC), Canada G1K 7P4; javad.mashreghi{at}mat.ulaval.ca, ransford{at}mat.ulaval.ca |
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Abstract: | Let (an)n0 be a sequence of complex numbers, and, for n0, let
A number of results are proved relating the growth of the sequences(bn) and (cn) to that of (an). For example, given p0, if bn= O(np and for all > 0,then an=0 for all n > p. Also, given 0 < p < 1, then for all > 0 if and onlyif . It is further shown that, given rß > 1, if bn,cn=O(rßn), then an=O(n),where , thereby proving a conjecture of Chalendar, Kellay and Ransford. The principal ingredientsof the proogs are a Phragmén-Lindelöf theorem forentire functions of exponential type zero, and an estimate forthe expected value of e(X), where X is a Poisson random variable.2000 Mathematics Subject Classification 05A10 (primary), 30D15,46H05, 60E15 (secondary). |
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