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