GEOMETRIZATION OF NUMERATION SYSTEMS

numeration systems, Ostrowski-Zeckendorf representation, geometrization theorem

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6. Gricenko S. A. & Mot’kina N. N. 2009. "Zadacha Hua-Lokena s prostymi chislami special’nogo vida", DAN respubliki Tadzhikistan, Vol. 52, no. 7, pp. 497-500. (Russian)

7. Gricenko S. A. & Mot’kina N. N. 2011. "On the computation of some singular series", Chebyshevskii sbornik, Vol. 12, no. 4, pp. 85-92. (Russian)

8. Gricenko S. A. & Mot’kina N. N. 2010. "O nekotoryh additivnyh zadachah teorii chisel", Nauchnye vedomosti BelGU. Serija Matematika. Fizika, Vol. 5(76), no. 18, pp. 83-87. (Russian)

9. Gricenko S. A. & Mot’kina N. N. 2011. "On Chudakov’s theorem involving primers of a special type", Chebyshevskii sbornik, Vol. 12, no. 4, pp. 75-84. (Russian)

10. Gricenko S. A. & Mot’kina N. N. 2009. "Ob odnom variante ternarnoj problemy Gol’dbaha", DAN respubliki Tadzhikistan, Vol. 52, no. 6, pp. 413-417. (Russian)

11. Gricenko S. A. & Mot’kina N. N. 2014. "Waring’s promblem involving natural numbers of a special type", Chebyshevskii sbornik, Vol. 15, no. 3, pp. 31-47. (Russian)

12. Davletjarova E. P. , Zhukova A. A. & Shutov A. V. 2013. "Geometrizacija sistemy schislenija Fibonacci i ee prilozhenija k teorii chisel", Algebra i analiz, Vol. 25, no. 6, pp. 1-23. (Russian) translation in St. Petersburg Mathematical Journal, 2014, 25:6, 893-907. doi:10. 1090/S10610022-2014-01321-0.

13. Davletjarova E. P. , Zhukova A. A. & Shutov A. V. 2016. "Geometrizacija obobshhennyh sistem schislenija Fibonacci i ee prilozhenija k teorii chisel", Chebyshevskii sbornik, Vol. 17, no. 2, pp. 88-112. (Russian)

14. Zhuravlev V. G. 2007. "Odnomernye kvazireshetki Fibonachchi i ih prilozhenija k diofantovym uravnenijam i algoritmu Evklida", Algebra i analiz, Vol. 19, no. 3, pp. 177-208. (Russian) translation in St. Petersburg Mathematical Journal, 2008, 19:3, 431-454. doi:10. 1090/S10610022-08-01005-4.

15. Zhuravlev V. G. 2007. "Odnomernye razbienija Fibonacci", Izv. RAN. Ser. matem. , Vol. 71, no. 2, pp. 89-122. (Russian) translation in Izvestiya: Mathematics, 2007, 71:2, 307-340. doi: 10. 1070/IM2007v071n02ABEH002358.

16. Zhuravlev V. G. 2006. "Summy kvadratov nad ∘-kol’com Fibonachchi", Zapiski nauchnogo seminara POMI, Vol. 337, pp. 165-190. (Russian) translation in Journal of Mathematical Sciences, 2007, 143:3, 3108-3123. doi: 10. 1007/s10958-007-0195-1.

17. Zhuravlev V. G. 2008. "Uravnenie Pellja nad ∘-kol’com Fibonachchi", Zapiski nauchnogo seminara POMI, Vol. 350, pp. 139-159. (Russian) translation in Journal of Mathematical Sciences, 2008, 150:3, 2084-2095. doi: 10. 1007/s10958-008-0123-z.

18. Zhuravlev V. G. 2008. "Chetno-fibonachchevy chisla: binarnaja additivnaja zadacha, rasprdelenie po progressijam i spectr", Algebra i analiz, Vol. 20, no. 3, pp. 18-46. (Russian) translation in St. Petersburg Mathematical Journal, 2009, 20:3, 339-360. doi: 10. 1090/S10610022-09-01051-6.

19. Krasil’shhikov V. V. & Shutov A. V. 2007. "Nekotorye voprosy vlozhenija reshetok v odnomernye kvaziperiodicheskie razbienija", Vestnik SamGU. Estestvennonauchnaja serija, no. 7(57), pp. 84-91. (Russian)

20. Krasil’shhikov V. V. & Shutov A. V. 2009. "Odnomernye kvaziperiodicheskie razbienija, dopuskajushhie vlozhenie progressij", Izvestija vuzov. Matematika, no. 7, pp. 3-9. (Russian). translation in Russian Mathematics, 2009, 53:7, 1-6. doi: 10. 3103/S1066369X09070019.

21. Manujlov N. N. 2001. "Rekurrentnye samopodobnye razbienija", Chebyshevskii sbornik, Vol. 4, no. 2, pp. 87-91. (Russian)

22. Matijasevich Ju. V. 1968. "Svjaz’ sistem uravnenij v slovah i dlinah s 10-j problemoj Gilberta", Zapiski nauchnyh seminarov LOMI, Vol. 8, pp. 132-144. (Russian)

23. Matijasevich Ju. V. 1968. "Dve redukcii 10-j problemy Gilberta", Zapiski nauchnyh seminarov LOMI, Vol. 8, pp. 145-158. (Russian)

24. Shvagireva I. K. 2010. "Binarnye additivnye zadachi nad ∘-progessijami Fibonachchi", Materialy VII mezhdunarodnoj konferencii "Algebra i teorija chisel: sovremennye problemy i prilozhenija posvjashhennoj pamjati professora Anatolija Alekseevicha Karatsuby, Tula, 11-16 maja 2010 goda TGPU, Tula, pp. 198-200. (Russian)

25. Shutov A. V. 2010. "Arifmetika i geometrija odnomernyh kvazireshetok", Chebyshevskii sbornik, Vol. 11, pp. 255-262. (Russian)

26. Shutov A. V. 2010. "Neodnorodnye diofantovy priblizhenija i raspredelenie drobnyh dolej", Fundamental’naja i prikladnaja matematika, Vol. 16, no. 6, pp. 189-202. (Russian) translation in Journal of Mathematical Sciences (New York), 2012, 182:4, 576-585. doi: 10. 1007/s10958012-0762-y.

27. Shutov A. V. 2004. "O raspredelenii drobnyh dolej", Chebyshevskii sbornik, Vol. 5, no. 3, pp. 112-121. (Russian)

28. Shutov A. V. 2005. "O raspredelenii drobnyh dolej II", Issledovanija po algebre, teorii chisel, funkcional’nomu analizu i smezhnym voprosam, no. 3, pp. 146-158. (Russian)

29. Shutov A. V. 2013. "Ob odnoj additivnoj zadache s drobnymi doljami", Nauchnye vedomosti BelGU. Serija Matematika. Fizika, Vol. 5(148), no. 30, pp. 111-120. (Russian)

30. Shutov A. V. 2004. "Perenormirovki vrashhenij okruzhnosti", Chebyshevskii sbornik, Vol. 5, no. 4, pp. 125-143. (Russian)

31. Shutov A. V. 2007. "Posledovatel’nosti Shturma: grafy Rozi i forsing", Chebyshevskii sbornik, Vol. 8, no. 2, pp. 128-139. (Russian)

32. Shutov A. V. 2004. "Proizvodnye povorotov okruzhnosti i podobie orbit", Zapiski nauchnyh seminarov POMI, Vol. 314, pp. 272-284. (Russian) translation in Journal of Mathematical Sciences, 2006, 133:6, 1765-1771. doi: 10. 1007/s10958-006-0088-8.

33. Shutov A. V. 2006. "Sistemy schislenija i mnozhestva ogranichennogo ostatka", Chebyshevskii sbornik, Vol. 7, no. 3, pp. 110-128. (Russian)