Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2013_25_6_a0, author = {E. P. Davletyarova and A. A. Zhukova and A. V. Shutov}, title = {Geometrization of {Fibonacci} numeration system and its applications to number theory}, journal = {Algebra i analiz}, pages = {1--23}, publisher = {mathdoc}, volume = {25}, number = {6}, year = {2013}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2013_25_6_a0/} }
TY - JOUR AU - E. P. Davletyarova AU - A. A. Zhukova AU - A. V. Shutov TI - Geometrization of Fibonacci numeration system and its applications to number theory JO - Algebra i analiz PY - 2013 SP - 1 EP - 23 VL - 25 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2013_25_6_a0/ LA - ru ID - AA_2013_25_6_a0 ER -
E. P. Davletyarova; A. A. Zhukova; A. V. Shutov. Geometrization of Fibonacci numeration system and its applications to number theory. Algebra i analiz, Tome 25 (2013) no. 6, pp. 1-23. http://geodesic.mathdoc.fr/item/AA_2013_25_6_a0/
[1] Vinogradov I. M., “Novyi metod v analiticheskoi teorii chisel”, Tr. Mat. in-ta AN SSSR, 10, 1937, 5–122 | Zbl
[2] Grekhem R., Knut D., Patashnik O., Konkretnaya matematika, Mir, M., 1998
[3] Gritsenko S. A., Motkina N. N., “Zadacha Khua Lokena s prostymi chislami spetsialnogo vida”, Dokl. AN Resp. Tadzhikistan, 52:7 (2009), 497–500
[4] Gritsenko S. A., Motkina N. N., “O nekotorykh additivnykh zadachakh teorii chisel”, Nauch. vedomosti BelGU. Ser. Mat. Fiz., 5(76):18 (2010), 83–87
[5] Gritsenko S. A., Motkina N. N., “Ob odnom variante ternarnoi problemy Goldbakha”, Dokl. AN Resp. Tadzhikistan, 52:6 (2009), 413–417
[6] Zhuravlev V. G., “Odnomernye kvazireshetki Fibonachchi i ikh prilozheniya k diofantovym uravneniyam i algoritmu Evklida”, Algebra i analiz, 19:3 (2007), 151–182 | MR | Zbl
[7] Zhuravlev V. G., “Odnomernye razbieniya Fibonachchi”, Izv. RAN. Ser. mat., 71:2 (2007), 89–122 | DOI | MR | Zbl
[8] Zhuravlev V. G., “Summy kvadratov nad $\circ$-koltsom Fibonachchi”, Zap. nauch. semin. POMI, 337, 2006, 165–190 | MR | Zbl
[9] Zhuravlev V. G., “Uravnenie Pellya nad $\circ$-koltsom Fibonachchi”, Zap. nauch. semin. POMI, 350, 2007, 139–159 | MR
[10] Zhuravlev V. G., “Chetno-fibonachchevy chisla: binarnaya additivnaya zadacha, raspredelenie po progressiyam i spektr”, Algebra i analiz, 20:3 (2008), 18–46 | MR | Zbl
[11] Keipers L., Niderreiter G., Ravnomernoe raspredelenie posledovatelnostei, Mir, M., 1985 | MR
[12] Krasilschikov V. V., Shutov A. V., “Nekotorye voprosy vlozheniya reshetok v odnomernye kvaziperiodicheskie razbieniya”, Vestnik SamGU. Estestvennonauch. ser., 2007, no. 7(57), 84–91
[13] Krasilschikov V. V., Shutov A. V., “Odnomernye kvaziperiodicheskie razbieniya, dopuskayuschie vlozhenie progressii”, Izv. vuzov. Mat., 2009, no. 7, 3–9 | MR | Zbl
[14] Matiyasevich Yu. V., “Svyaz sistem uravnenii v slovakh i dlinakh s 10-i problemoi Gilberta”, Zap. nauch. semin. LOMI, 8, 1968, 132–144 | MR | Zbl
[15] Matiyasevich Yu. V., “Dve reduktsii 10-i problemy Gilberta”, Zap. nauch. semin. LOMI, 8, 1968, 145–158 | MR | Zbl
[16] Shvagireva I. K., “Binarnye additivnye zadachi nad $\circ$-progressiyami Fibonachchi”, Materialy VII mezhdunar. konf. “Algebra i teoriya chisel: sovremennye problemy i prilozheniya”, posvyaschennoi pamyati prof. A. A. Karatsuby (Tula, 11–16 maya, 2010), TGPU, Tula, 2010, 198–200
[17] Shutov A. V., “Arifmetika i geometriya odnomernykh kvazireshetok”, Chebyshevskii sb., 11:1 (2010), 255–262 | MR | Zbl
[18] Shutov A. V., “Neodnorodnye diofantovy priblizheniya i raspredelenie drobnykh dolei”, Fundamentalnaya i prikladnaya matematika, 16:6 (2010), 189–202 | MR
[19] Shutov A. V., “O raspredelenii drobnykh dolei”, Chebyshevskii sb., 5:3 (2004), 112–121 | MR | Zbl
[20] Shutov A. V., “O raspredelenii drobnykh dolei. II”, Issledovaniya po algebre, teorii chisel, funktsionalnomu analizu i smezhnym voprosam, Vyp. 3, 2005, 146–158
[21] Shutov A. V., “Ob odnoi additivnoi zadache s chislami spetsialnogo vida”, Matematika, informatika i metodika ikh prepodavaniya, Materialy Vserossiiskoi konf., posvyaschennoi 110-letiyu matematicheskogo fakulteta MPGU, M., 2011, 102–104
[22] Shutov A. V., “Ob odnoi additivnoi zadache s drobnymi dolyami”, Nauch. vedomosti BelGU. Ser. Mat. Fiz., 5(148):30 (2013), 111–120
[23] Shutov A. V., “Perenormirovki vraschenii okruzhnosti”, Chebyshevskii sb., 5:4 (2004), 125–143 | MR | Zbl
[24] Shutov A. V., “Posledovatelnosti Shturma: grafy Rozi i forsing”, Chebyshevskii sb., 8:2 (2007), 128–139 | MR | Zbl
[25] Shutov A. V., “Proizvodnye povorotov okruzhnosti i podobie orbit”, Zap. nauch. semin. POMI, 314, 2004, 272–284 | MR | Zbl
[26] Shutov A. V., “Sistemy schisleniya i mnozhestva ogranichennogo ostatka”, Chebyshevskii sb., 7:3 (2006), 110–128 | MR | Zbl
[27] Hecke E., “Eber Analytische Funktionen und die Verteilung van Zahlen mod Eins”, Math. Sem. Hamburg Univ., 5 (1921), 54–76
[28] Knuth D. E., “Fibonacci multiplication”, Appl. Math. Lett., 1:1 (1988), 57–60 | DOI | MR | Zbl
[29] Pinner C. G., “On sums of fractional parts $\{n\alpha+\gamma\}$”, J. Number Theory, 65:1 (1997), 48–73 | DOI | MR | Zbl
[30] van Ravenstein T., “The three gap theorem (Steinhaus conjecture)”, J. Austral. Math. Soc. Ser. A, 45:3 (1988), 360–370 | DOI | MR | Zbl
[31] Shutov A. V., “New estimates in the Hecke–Kesten problem”, Analytic and Probabilistic Methods in Number Theory, TEV, Vilnius, 2007, 190–203 | MR | Zbl
[32] Weyl H., “Über die Gibbs'sche Erscheinung und verwandte Konvergenzphänomene”, Rend. Circ. Mat. Palermo, 30 (1910), 377–407 | DOI | Zbl