본문 바로가기
KERD
논문KCI 등재

Arithmetic functions in algebra, geometry and analysis

E. Egri|J. Sandor
장전수학회 (Jangjeon Mathematical Society)|2007.04|Advanced Studies in Contemporary Mathematics|제14권 제2호|pp. 161-213

1

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

Abstract

This is a survey paper on certain classical or new arithmetic functions with connections and/or applications in Algebra, Geometry or Analysis. We want to show the importance of certain parts of Number theory (especially, of arithmetical functions) to these major elds of Mathematics. The survey is focused especially on the author's results, and in the course of presentations, many new results (with proofs) will be pointed out, too.

참고문헌 (68)

  1. C. ADIGA, "On a generalization of Sandor's function", 5, pp.121~124 (2002)
  2. T. M. APOSTOL, "An introduction to analytic number theory" (1976), Springer Verlag
  3. K. T. ATANASSOV, "On some modifications of ？ and ' functions", 48, pp.41~44 (1989)
  4. E. T. AVANESOV, "A certain problem of Steinhaus", 21, pp.29~32 (1971)
  5. E.T. BELL, "An arithmetical theory of certain numerical functions" (1915)
  6. R. BOJANIC, "Asymptotic evaluations of the sum of divisors of certain numbers" (1954)
  7. E. D CASHWELL, "The ring of number theoretic functions", 9, pp.975~985 (1959)
  8. K. CHIKAWA et al, "On a problem of Steinhaus" (1962), Acta Arith. VII
  9. K. CHIKAWA et al, "Computation of cyclic parts of Steinhaus problem for powers" (1962), Acta Arith. VII
  10. E. COHEN, "Arithmetic functions associated with the unitary divisors of an integer", 74, pp.66~80 (1960)
  11. G. L. COHEN, "Harmonic seeds", 36, pp.386~390 (1998)
  12. G. L. COHEN, "On a generalization of Ore's harmonic numbers", 16(3), pp.161~172 (1998)
  13. M. DEACONESCU, "Particular letter to J. Sandor"
  14. M. DEACONESCU, "Variations on a theme by Hurwitz" (1987)
  15. L. E. DICKSON, "History of the theory of numbers", 1, pp.113~ (1971)
  16. J. EARLS, "Some Smarandache-type sequences and problems concerning abundentand de？cient numbers", 14, pp.243~250 (2004)
  17. K. FORD, "Math Pages"
  18. L. GEGENBAUER, "？ Uber ein theorem des Hernn Mac Mahon", 11, pp.287~288 (1900)
  19. P. HAGIS, "Unitary harmonic numbers", 51, pp.1~7 (1975)
  20. G. H. HARDY, "An introduction to the theory of numbers" (1979), Oxford at the Clarendon Press
  21. Math. Student 61, "A note on generalized multiplicative and generalized additivearithmetic functions" (1992)
  22. I. M. ISAACS, "Character theory of finite groups" (1976), Academic Press
  23. K. ISEKI, "A problem of number theory", 36, pp.578~580 (1960)
  24. K. NAGESWARA RAO, "On some unitary divisor functions", 28, pp.347~351 (1967)
  25. O. ORE,On the averages of the divisors of a number, "Amer. Math. Monthly", 55, pp.615~619 (1948)
  26. G. POLYA und G. SZEG} O, "Aufgaben und Lehrs？atze aus der Analysis" (1924), Leipzig
  27. G. D. POOLE, "Integers and the sum of the factorials of their digits", 44, pp.278~279 (1971)
  28. M. R. POURNAKI, "An extension of a result of Gauss to ？nite groups: a linearalgebraic approach", 61, pp.24~31 (2006)
  29. R. RIVEST,A. SHAMIR, "A method for obtaining digital signatures and public-key cryptosystems", 21, pp.120~126 (1978)
  30. J. SANDOR, "Handbook of number theory, II" (2004), Springer Verlag
  31. J. SANDOR, "On the arithmetical functions dk(n) and d？k(n)", 53, pp.107~115 (1996)
  32. J. SANDOR, "The M？obius function: generalizations and extensions", 6(2), pp.77~128 (2003)
  33. J. SANDOR, "On an exponential totint function", 41, pp.91~94 (1996)
  34. J. SANDOR, "On the work of Gy. V？alyi in number theory", (1), pp.5~9 (2005)
  35. J. SANDOR, "Some diophantine equations for pareticular arithmetic functions" (1989), Univ. Timi？soara
  36. J. S？and R. SIVARAMAKRISHAN, "The many facets of Euler's totient" (1993)
  37. J. SANDOR, "Note on Jordan's arithmetical function", pp.1~ (1989), Univ. Timi？soara
  38. J. SANDOR, "Elem. Math.", 44, pp.73~76 (1989)
  39. J. SANDOR, "On arithmetic functions and a trigonometrical product", 7(4), pp.6~9 (2001)
  40. J. SANDOR, "Handbook of number theory, I" (2005), Springer Verlag
  41. J. SANDOR, "On even perfect and superperfect numbers", 7(1), pp.4~5 (2001)
  42. J. SANDOR, "On multiplicatively perfect numbers", 2(1), pp.1~6 (2001)
  43. J. SANDOR, "Unpublished manuscripts on perfect numbers" (2004)
  44. J. SANDOR, "Selected chapters of Geometry, Analysis, and Number Theory" (2005), VictoriaUniv. of Technology
  45. J. SANDOR, "Biunitary harmonic numbers", 9(1), pp.17~ (2006)
  46. J. SANDOR, "On multiplicatively e-perfect numbers", 5(4) (2004)
  47. J. SANDOR, "On g.c.d. and l.c.m. of numbers", 15, pp.167~178 (1999)
  48. J. SANDOR, "Problem L : 836", pp.34~37
  49. J. SANDOR, "Geometric theorems, diophantine equations, and arithmetic functions" (2002), New Mexico
  50. J. SANDOR, "On certain generalizations of the Smarandache function", 5(2), pp.41~51 (1999)
  51. J. SANDOR, "On certain generalizations of the Smarandache function", 11(1-3), pp.202~212 (2000)
  52. J. SANDOR, "The Euler minimum and maximum functions", 8(1) (2005)
  53. J. SANDOR, "The sum of divisors minimum and maximum functions", 8(1) (2005)
  54. J. SANDOR, "A note on the divisors minimum ？nction", 12(2A), pp.273~275 (2004)
  55. J. SANDOR, "The product of divisors minimum and maximum functions", 7(2), pp.11~ (2004)
  56. J. SANDOR, "The unitary totient minimum and maximum functions", (2), pp.91~100 (2005)
  57. J. SANDOR, "On an additive analogue of the function S", 7, pp.91~95 (2001)
  58. J. SANDOR, "An additive analogue of the Euler minimum function", 10(1), pp.53~62 (2005)
  59. J. SANDOR, "On certain special functions of Number theory and mathematical analysis" (2006)
  60. J. SANDOR, "On the composition of some arithmetic functions" (1989), Studia Univ. Babe？s-Bolyai
  61. H. STEINHAUS, "One hundred problems in elementary mathematics", pp.11~, PergamonPress L.T.D.
  62. E. G. STRAUS, "On exponential divisors", 41, pp.465~471 (1974)
  63. M. V. SUBBARAO, "Lecture Notes in Math.", (251) (1972)
  64. E. C. TITCHMARSH, "The theory of the Riemann zeta-function" (1951), Oxford Univ. Press
  65. R. VAIDYANATHASWAMY,The theory of multiplicative arithmetic functions, "Trans. Amer. Math. soc.", 33, pp.579~662 (1931)
  66. Gy. VALYI, "On the theory of curves of third order" (1890)
  67. Gy. VALYI, "？ Uber die Fusspunktdreiecke", 14, pp.243~252 (1903)
  68. Ch. R. WALL,Unitary harmonic numbers, "Fib. Quart", 21, pp.18~25 (1983)

관련 논문AI추천

Arithmetic of the modular functions $j_{1,2}$ and $j_{1,3}$구자경, 김창헌대한수학회 · 대한수학회보2007 · 제44권 제1호Some estimates of Littlewood-Paley type operators in arithmetic김용철대한수학회 · 대한수학회논문집2007 · 제22권 제4호Observations about algebraic dependence of Dirichlet seriesPatanee Udomkavanich, Pattira Ruengsinsub, Vichian Laohakosol대한수학회 · 대한수학회지2005 · 제42권 제4호On the Euler minimum and maximum functionsJozsef Sandor장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제2호Some Results for Unified Riemann-Zeta FunctionA. PARASHAR, S. P. GOYAL경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제1호Arithmetic of infinite products and Rogers-Ramanujan continued fractions구자경, 김대열, Yilmaz Simsek대한수학회 · 대한수학회논문집2007 · 제22권 제3호

이 간행물의 다른 논문 (10건)

Some subclasses of multivalent functions involving a certain linear operatorH. Silverman, M. K. Aouf, H. M. Srivastavapp. 215-232A note on p -adic q -Euler measureY. Simsek, H. Ozden, S.-H. Rim, I. Cang？lpp. 233-240Explicit p-adic expansion for alternating sums of powersS.-H. Rim, T. Kimpp. 241-250On the additive structure of the set of quadratic residues modulo pM. Demirci, N. Y. Ikikardes, G. Soydan, I. Cang？lpp. 251-257Triple bisection algorithms for 1-D utility elicitation in the case of monotonic preferenceK. I. Tenekedjievpp. 259-281
원문 보기