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On an Oscillatory Result for the Coefficients of General Dirichlet Series

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From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Part of the book series: Developments in Mathematics ((DEVM,volume 28))

Abstract

Let (a n ) n≥1 be a sequence of real numbers. Then we say that (a n ) n≥1 is oscillatory if there exist infinitely many n with a n >0 and infinitely many n with a n <0.

Mathematics Subject Classification: Primary 11M41, 30B50

The second author’s work was supported (in part) by The City University of New York PSC-CUNY Research Award Program (grant #62571-00 40 and grant #63516–00 41).

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References

  1. G.H. Hardy and M. Riesz: The General Theory of Dirichlet’s Series, Dover, New York, 2005.

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  2. E.N. Laguerre: Sur la théorie des équations numériques, J. Math. Pures Appl. 9 (1883), 99–146.

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  3. W. Pribitkin: On the sign changes of coefficients of general Dirichlet series, Proc. Amer. Math. Soc. 136 (2008), 3089–3094.

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  4. W. Pribitkin: On the oscillatory behavior of certain arithmetic functions associated with automorphic forms, J. Number Theory 131 (2011), 2047–2060.

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Acknowledgements

The authors thank the referee for making useful suggestions.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, INF 288, 69120, Heidelberg, Germany

    Winfried Kohnen

  2. Department of Mathematics, College of Staten Island, CUNY, 2800 Victory Boulevard, Staten Island, NY, 10314, USA

    Wladimir de Azevedo Pribitkin

Authors
  1. Winfried Kohnen
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  2. Wladimir de Azevedo Pribitkin
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Corresponding author

Correspondence to Wladimir de Azevedo Pribitkin .

Editor information

Editors and Affiliations

  1. , Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Hershel M. Farkas

  2. , Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, 08544, New Jersey, USA

    Robert C. Gunning

  3. , Department of Mathematics, Temple University, Wachman Hall 608, Philadelphia, 19122, Pennsylvania, USA

    Marvin I. Knopp

  4. , Department of Mathematics, University of Michigan, Church St. 530, Ann Arbor, 48109, Michigan, USA

    B. A. Taylor

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In memory of Leon Ehrenpreis, so strong and full of brightness

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Kohnen, W., de Azevedo Pribitkin, W. (2013). On an Oscillatory Result for the Coefficients of General Dirichlet Series. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_18

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