Journal of applied mathematics & informatics

  • 제41권6호
  • /
  • Pages.1227-1235
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  • 2023
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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CONVOLUTION SUM OF DIVISOR FUNCTIONS GIVEN THE CONDITIONS OF COPRIME

  • SOUNG DOUK LEE (Department of Mathematics Education, Kong Ju National University) ;
  • DAEYEOUL KIM (Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University)
  • 투고 : 2023.03.14
  • 심사 : 2023.09.13
  • 발행 : 2023.11.30
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초록

The study of convolution sums for divisor functions is an area that has been extensively researched by many mathematicians including Ramanujan. The aim of this paper is to find the formula for convolution sum of divisor functions with coprime conditions.

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과제정보

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2021R1F1A1051093).

참고문헌

  1. A. Dujella, Number Theory, Skolska knjiga, Zagreb, 2021.
  2. H.M. Farkas, On an arithmetical function, Contemp. Math. 382 (2005), 121-130. https://doi.org/10.1090/conm/382/07052
  3. J.W.L. Glaisher, On certain sums of products of quantities depending upon the divisors of a number, Mess. Math. 15 (1885), 1-20.
  4. S. Kong, Y. Li and D. Kim, Convolution sums of restricted divisor functions derived from Dirichlet convolution, preprint.
  5. P.J. McCarthy, Introduction to arithmetical functions, Springer Science and Business Media, 2012.
  6. M.B. Nathanson, Additive Number Theory, The Classical Bases, Graduate Texts in Mathematics 164, Springer, 1996.
  7. S. Ramanujan, Collect papers, AMS Chelsea Publishing, Province, RI, USA, 2000.
  8. 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
  9. K.S. Williams, Number Theory in the Spirit of Liouville, London Mathematical Society, Student Texts 76, Cambridge, 2011.