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Eigenvalues of diffusion operators and Prime numbers

Year 2017, , 488 - 491, 30.09.2017
https://doi.org/10.17776/csj.340494

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.

References

  • [1]. M. Abramowitz, I. A. Stegun; Handbook of Mathematical Functions, Dover Publications, New York, 1972.
  • [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]. 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]. 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.
  • [9]. P. Dusart; Autour de la fonction qui compte le nombre de nombres premiers, Ph.D. thesis. Universite de Limoges, (1998).
  • [10]. J. E. Littlewood; Sur la distribution des nombres premiers, Comptes Rendus 158 (1914),1869-1872.
  • [11]. Amirov RK, Çakmak Y, Gulyaz S: Boundary value problem for second order differential equations with Coulomb singularity on a finite interval. Indian J. Pure Appl. Math. (2006), 37: 125-140.
  • [12]. Panaitopol, L. "A formula for pi(x) applied to a result of Koninck-Ivic." Nieuw Archief voor Wiskunde 1 (2000), 55-56.

Difüzyon Operatörlerinin Özdeğerleri ve Asal Sayılar

Year 2017, , 488 - 491, 30.09.2017
https://doi.org/10.17776/csj.340494

Abstract

Bu makalede,
difüzyon operatörlerinin pozitif özdeğerleri ile asal sayılar arasındaki
ilişki incelenmiştir. Ayrıca, özdeğerleri, asal sayıların dağılımını gösteren
Coulomb singularitesine sahip bir Sturm-Liouville problemi önerilmiştir.

References

  • [1]. M. Abramowitz, I. A. Stegun; Handbook of Mathematical Functions, Dover Publications, New York, 1972.
  • [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]. 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]. 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.
  • [9]. P. Dusart; Autour de la fonction qui compte le nombre de nombres premiers, Ph.D. thesis. Universite de Limoges, (1998).
  • [10]. J. E. Littlewood; Sur la distribution des nombres premiers, Comptes Rendus 158 (1914),1869-1872.
  • [11]. Amirov RK, Çakmak Y, Gulyaz S: Boundary value problem for second order differential equations with Coulomb singularity on a finite interval. Indian J. Pure Appl. Math. (2006), 37: 125-140.
  • [12]. Panaitopol, L. "A formula for pi(x) applied to a result of Koninck-Ivic." Nieuw Archief voor Wiskunde 1 (2000), 55-56.
There are 12 citations in total.

Details

Journal Section Articles
Authors

Rauf Amirov

İbrahim Adalar

Publication Date September 30, 2017
Submission Date May 29, 2017
Acceptance Date August 7, 2017
Published in Issue Year 2017

Cite

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