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A class of arithmetic functions on PSL2(Z)

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In [3] and [2], Atanassov introduced the two arithmetic func- tions [수식] called the irrational factor and the restrictive factor, respectively. Alkan, Ledoan, Panaitopol, and the authors explore properties of these arith- metic functions in [1], [7], [8] and [9]. In the present paper, we generalize these functions to a larger class of elements of PSL2(Z), and explore some of the properties of these maps.

Abstract

In [3] and [2], Atanassov introduced the two arithmetic func- tions [수식] called the irrational factor and the restrictive factor, respectively. Alkan, Ledoan, Panaitopol, and the authors explore properties of these arith- metic functions in [1], [7], [8] and [9]. In the present paper, we generalize these functions to a larger class of elements of PSL2(Z), and explore some of the properties of these maps.

참고문헌 (13)

  1. E. Alkan, "Asymptotic behavior of the irrational factor", Acta Math. Hungar, 121(3), pp.293~305 (2008)
  2. K. T. Atanassov, "Restrictive factor: definition, properties and problems", Notes Number Theory Discrete Math, 8(4), pp.117~119 (2002)
  3. K. T. Atanassov, "Irrational factor: definition, properties and problems", Notes Number Theory Discrete Math, 2(3), pp.42~44 (1996)
  4. F. Boca, "On the distribution of the free path length of the linear flow in a honeycomb", Ann. Inst. Fourier, 59(3), pp.1043~1075 (2009)
  5. G. H. Hardy, "An Introduction to the Theory of Numbers, In With a foreword by Andrew Wiles" (2008), Oxford University Press
  6. N. M. Korobov, "Estimates of trigonometric sums and their applications", Uspehi Mat. Nauk, 13(4), pp.185~192 (1958)
  7. A. Ledoan, "Real moments of the restrictive factor", Proc. Indian Acad. Sci. Math. Sci, 119(4), pp.559~566 (2009)
  8. L. Panaitopol, "Properties of the Atanassov functions", Adv. Stud. Contemp. Math, 8(1), pp.55~58 (2004)
  9. P. Spiegelhalter, "Strong and weak Atanassov pairs", Proc. Jangjeon Math. Soc, 14(3), pp.355~361 (2011)
  10. E. C. Titchmarsh, "The Theory of Functions" (1939), Oxford University Press
  11. E. C. Titchmarsh, "The theory of the Riemann zeta-function" (1986), The Clarendon Press Oxford University Press
  12. I. M. Vinogradov, "A new estimate of the function ζ(1+it)", Izv. Akad. Nauk SSSR. Ser. Mat, 22, pp.161~164 (1958)
  13. A. Walfisz, "Weylsche Exponentialsummen in der neueren Zahlentheorie" (1963), VEB Deutsche Verlag der Wissenschaften

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