Geodesic
Differentiability of the Minkowski function $?(x)$.~II
Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 957-989.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove new theorems on the derivative of the Minkowski function.
Keywords: Minkowski's function, derivative, continued fraction
Mots-clés : continuant. 
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I. D. Kan. Differentiability of the Minkowski function $?(x)$.~II. Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 957-989. http://geodesic.mathdoc.fr/item/IM2_2019_83_5_a2/

[1] H. Minkowski, Gesammelte Abhandlungen, v. 2, B. G. Teubner, Leipzig–Berlin, 1911, iv+466 pp. | Zbl

[2] R. Salem, “On some singular monotonic functions which are strictly increasing”, Trans. Amer. Math. Soc., 53:3 (1943), 427–439 | DOI | MR | Zbl

[3] J. R. Kinney, “Note on a singular function of Minkowski”, Proc. Amer. Math. Soc., 11:5 (1960), 788–794 | DOI | MR | Zbl

[4] P. Viader, J. Paradis, L. Bibiloni, “A new light on Minkowski's $?(x)$ function”, J. Number Theory, 73:2 (1998), 212–227 | DOI | MR | Zbl

[5] J. Paradis, P. Viader, L. Bibiloni, “The derivative of Minkowski's $?(x)$ function”, J. Math. Anal. Appl., 253:1 (2001), 107–125 | DOI | MR | Zbl

[6] A. A. Dushistova, N. G. Moshchevitin, “On the derivative of the Minkowski question mark function $?(x)$”, J. Math. Sci. (N.Y.), 182:4 (2012), 463–471 | DOI | MR | Zbl

[7] A. A. Dushistova, I. D. Kan, N. G. Moshchevitin, “Differentiability of the Minkowski question mark function”, J. Math. Anal. Appl., 401:2 (2013), 774–794 | DOI | MR | Zbl

[8] D. R. Gayfulin, “Derivatives of two functions belonging to the Denjoy–Tichy–Uitz family”, St. Petersburg Math. J., 27:1 (2016), 51–85 | DOI | MR | Zbl

[9] A. Ya. Khinchin, Continued fractions, The Univ. of Chicago Press, Chicago, Ill.–London, 1964, xi+95 pp. | MR | MR | Zbl | Zbl

[10] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete mathematics. A foundation for computer science, 2nd ed., Addison-Wesley Publ. Co., Reading, MA, 1994, xiv+657 pp. | MR | Zbl

[11] I. D. Kan, “Methods for estimating continuants”, J. Math. Sci. (N.Y.), 182:4 (2012), 508–517 | DOI | MR | Zbl

[12] I. D. Kan, “A refinement of the rule of comparing continuants”, Discrete Math. Appl., 10:5 (2000), 477–480 | DOI | DOI | MR | Zbl

[13] T. S. Motzkin, E. G. Straus, “Some combinatorial extremum problems”, Proc. Amer. Math. Soc., 7:6 (1956), 1014–1021 | DOI | MR | Zbl

[14] D. E. Knuth, The art of computer programming, v. 2, Seminumerical algorithms, 3rd ed., Addison-Wesley, Reading, MA, 1998, xiv+762 pp. | MR | MR | Zbl | Zbl