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On the sign changes of coefficients of general Dirichlet series
Author(s):
Wladimir
de Azevedo
Pribitkin
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3089-3094.
MSC (2000):
Primary 11M41, 30B50
Posted:
April 30, 2008
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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:
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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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