Research Article

Eigenvalues of diffusion operators and Prime numbers

Volume: 38 Number: 3 September 30, 2017
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Eigenvalues of diffusion operators and Prime numbers

Abstract

In this paper, the relationship between the positive eigenvalues of diffusion operators and prime numbers is investigated. We also propose a Sturm-Liouville problem with Coulomb singularity that shows eigenvalues the distribution of prime numbers.

Keywords

References

  1. [1]. M. Abramowitz, I. A. Stegun; Handbook of Mathematical Functions, Dover Publications, New York, 1972.
  2. [2]. M. G. Gasymov and G. Sh. Guseinov, Determination of diffusion operator on spectral data, Dokl. Akad. Nauk Azerb. SSR, 37(2) (1981), 19-23.
  3. [3]. B. Mingarelli; A note on Sturm-Liouville problems whose spectrum is the set of prime numbers, Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 123, 1-4.
  4. [4]. Amirov Rauf; Adalar Ibrahim, Eigenvalues of Sturm-Liouville operators and prime numbers. Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 50, 1-3.
  5. [5]. E. Ingham; The distribution of prime numbers, Cambridge Mathematical Librairy, Cambridge University Press, Cambridge, 1990. Reprint of the 1932 original, With a foreword by R. C. Vaughan.
  6. [6]. P. T. Bateman and H. G. Diamond, Analytic Number Theory, World Scientific, Hackensack, NJ, 2004.
  7. [7]. S. A. Buterin and V. A. Yurko, Inverse problems for second-order differential pencils with Dirichlet boundary conditions, Journal of Inverse and III-Posed Problems 20 (2012), 855–881.
  8. [8]. Guo, Yongxia, and Guangsheng Wei. "Determination of differential pencils from dense nodal subset in an interior subinterval." Israel Journal of Mathematics 206.1 (2015), 213-231.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Rauf Amirov

Publication Date

September 30, 2017

Submission Date

May 29, 2017

Acceptance Date

August 7, 2017

Published in Issue

Year 1970 Volume: 38 Number: 3

APA
Amirov, R., & Adalar, İ. (2017). Eigenvalues of diffusion operators and Prime numbers. Cumhuriyet Science Journal, 38(3), 488-491. https://doi.org/10.17776/csj.340494

Cited By

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