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

 

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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Additional Information

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: pribitkin@mail.csi.cuny.edu, w\_pribitkin@msn.com

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09296-4
PII: S 0002-9939(08)09296-4
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.