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On the sign changes of coefficients of general Dirichlet series

Author: Wladimir de Azevedo Pribitkin
Journal: Proc. Amer. Math. Soc. 136 (2008), 3089-3094
MSC (2000): Primary 11M41, 30B50
Published electronically: April 30, 2008
MathSciNet review: 2407071
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Abstract: Under what conditions do the (possibly complex) coefficients of a general Dirichlet series exhibit oscillatory behavior? In this work we invoke Laguerre's Rule of Signs and Landau's Theorem to provide a rather simple answer to this question. Furthermore, we explain how our result easily applies to a multitude of functions.

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Wladimir de Azevedo Pribitkin
Affiliation: Department of Mathematics, College of Staten Island, City University of New York, 2800 Victory Boulevard, Staten Island, New York 10314
Email:, w\

Keywords: General Dirichlet series, oscillatory sequence, Mellin transform
Received by editor(s): July 23, 2007
Received by editor(s) in revised form: July 29, 2007
Published electronically: April 30, 2008
Additional Notes: This work was supported (in part) by The City University of New York PSC-CUNY Research Award Program (grant #68327-00 37).
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.