Journal of applied mathematics & informatics

  • 제41권3호
  • /
  • Pages.553-567
  • /
  • 2023
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

CHANGING RELATIONSHIP BETWEEN SETS USING CONVOLUTION SUMS OF RESTRICTED DIVISOR FUNCTIONS

  • ISMAIL NACI CANGUL (Department of Mathematics, Bursa Uludag University) ;
  • DAEYEOUL KIM (Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University)
  • 투고 : 2022.08.01
  • 심사 : 2023.01.16
  • 발행 : 2023.05.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.

키워드

과제정보

The first author was supported by Bursa Uludag University Research Fund (Project No: KUAP (F) 2022/1049)) and the corresponding author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2021R1F1A1051093).

참고문헌

  1. B. Cho, Convolution sums of divisor functions for prime levels, Int. J. Number Theory 16 (2020), 537-546. https://doi.org/10.1142/S179304212050027X
  2. H.M. Farkas, On an arithmetical function, Ramanujan J. 8 (2004), 309-315. https://doi.org/10.1007/s11139-004-0141-5
  3. H.M. Farkas, On an arithmetical function II, Contemp. Math. 382 (2005), 121-130. https://doi.org/10.1090/conm/382/07052
  4. N.J. Fine, Basic hyper-geometric series and applications, American Mathematical Society, Providence, RI, 1988.
  5. P. Haukkanen, Derivation of arithmetical functions under the Dirichlet convolution, Int. J. Number Theory 14 (2018), 1257-1264. https://doi.org/10.1142/S1793042118500781
  6. J. Hwang, Y. Li and D. Kim, Arithmetic properties derived from coefficients of certain eta quotients, J. Ineq. Appl. 2020:104 (2020), 23 pages.
  7. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, GTM, Springer-Verlag, 1990.
  8. D. Kim and Y.K. Park, Certain combinatoric convolution sums involving divisor functions product formula, Taiwan J. Math. 18 (2014), 973-988.
  9. K. Matsuda, Note on a theorem of Farkas and Kra, The Ramanujan J. 53 (2020), 319-356. https://doi.org/10.1007/s11139-020-00301-x
  10. P.J. McCarthy, Introduction to arithmetical functions, Springer Science & Business Media, 2012.
  11. M.B. Nathanson, Additive Number Theory The Classical Bases, Graduate Texts in Mathematics, 164, Springer, 1996.
  12. E. Ntienjem, Elementary evaluation of convolution sums involving the divisor function for a class of levels, North-West. Eur. J. Math. 5 (2019), 101-165.
  13. S. Ramanujan, Collected papers, AMS Chelsea Publishing, Province, RI, USA, 2000.
  14. R. Vaidyanathaswamy, The theory of multiplicative arithmetic functions, Transactions of the American Mathematical Society 33 (1931), 579-662. https://doi.org/10.1090/S0002-9947-1931-1501607-1
  15. K.S. Williams, Number Theory in the Spirit of Liouville, London Mathematical Society, Student Texts 76, Cambridge, 2011.