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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]. M. Abramowitz, I. A. Stegun; Handbook of Mathematical Functions, Dover Publications, New York, 1972.
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- [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]. 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]. P. T. Bateman and H. G. Diamond, Analytic Number Theory, World Scientific, Hackensack, NJ, 2004.
- [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]. 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
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