Kovalyov, Ivan; Kunis, Stefan Two-dimensional moment problem and Schur algorithm. (English) Zbl 07974842 Integral Equations Oper. Theory 97, No. 1, Paper No. 5, 21 p. (2025). MSC: 30E05 44A60 30B70 14P99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fogg, N. Pytheas; Noûs, Camille Symbolic coding of linear complexity for generic translations on the torus, using continued fractions. (English) Zbl 07938121 J. Mod. Dyn. 20, 527-596 (2024). MSC: 37B10 37B51 11J70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berthé, V.; Dajani, K.; Kalle, C.; Krawczyk, E.; Kuru, H.; Thevis, A. Rational approximations, multidimensional continued fractions, and lattice reduction. (English) Zbl 07919514 Abdellatif, Ramla (ed.) et al., Women in numbers Europe IV. Research directions in number theory. Selected papers based on the presentations at the 4th workshop, WINE 4, Utrecht, the Netherlands, August 29 – September 2, 2022. Cham: Springer. Assoc. Women Math. Ser. 32, 111-154 (2024). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 11K50 11K55 11A55 11Y16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Řada, Hanka; Starosta, Štěpán; Kala, Vítězslav Periodicity of general multidimensional continued fractions using repetend matrix form. (English) Zbl 1542.11012 Expo. Math. 42, No. 3, Article ID 125571, 37 p. (2024). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11A55 11J70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Blackman, John; Dolan, James; Karpenkov, Oleg Multidimensional integer trigonometry. (English) Zbl 07902969 Commun. Math. 31, No. 2, 1-26 (2023). Reviewer: Steven T. Dougherty (Scranton) MSC: 11H06 11A55 52B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. Multidimensional continued fractions and symbolic codings of toral translations. (English) Zbl 1533.37040 J. Eur. Math. Soc. (JEMS) 25, No. 12, 4997-5057 (2023). MSC: 37B10 37A30 37A44 11J70 11K50 11A55 11Y65 28A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
German, O. N. Badly approximable matrices and Diophantine exponents. (English. Russian original) Zbl 1517.11074 Dokl. Math. 106, Part Suppl. 2, S201-S220 (2022); translation from Chebyshevskiĭ Sb. 14, No. 4(48), 38-79 (2013). MSC: 11J13 11J70 × Cite Format Result Cite Review PDF Full Text: DOI Link
Garrity, Thomas On Gauss-Kuzmin statistics and the transfer operator for a multidimensional continued fraction algorithm: the triangle map. (English) Zbl 1513.11144 Publ. Math. Debr. 101, No. 3-4, 263-280 (2022). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 11K50 11J70 37C30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chaika, Jon; Damanik, David; Fillman, Jake; Gohlke, Philipp Zero measure spectrum for multi-frequency Schrödinger operators. (English) Zbl 1518.47054 J. Spectr. Theory 12, No. 2, 573-590 (2022). MSC: 47B36 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sato, Yusuke Fujiki-Oka resolution for three-dimensional cyclic quotient singularities via binary trees. (English) Zbl 1516.14070 Tokyo J. Math. 45, No. 1, 69-87 (2022). Reviewer: Tomohiro Okuma (Yamagata) MSC: 14J17 05C05 14B05 14M25 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. Symmetry properties of karyon tilings. (English. Russian original) Zbl 1496.52023 J. Math. Sci., New York 264, No. 2, 150-182 (2022); translation from Zap. Nauchn. Semin. POMI 502, 74-121 (2021). Reviewer: Elizaveta Zamorzaeva (Chişinău) MSC: 52C22 11J70 11K50 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. Local structure of karyon tilings. (English. Russian original) Zbl 1496.52022 J. Math. Sci., New York 264, No. 2, 122-149 (2022); translation from Zap. Nauchn. Semin. POMI 502, 32-73 (2021). Reviewer: Elizaveta Zamorzaeva (Chişinău) MSC: 52C22 11K55 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Karpenkov, Oleg N. Geometry of continued fractions. 2nd edition. (English) Zbl 1487.11003 Algorithms and Computation in Mathematics 26. Berlin: Springer (ISBN 978-3-662-65276-3/hbk; 978-3-662-65277-0/ebook). xx, 451 p. (2022). MSC: 11-02 11J70 11A55 11H55 11K50 30B70 40A15 × Cite Format Result Cite Review PDF Full Text: DOI
Sato, Kohei; Sato, Yusuke Crepant property of Fujiki-Oka resolutions for Gorenstein abelian quotient singularities. (English) Zbl 1485.14004 Nihonkai Math. J. 32, No. 1, 41-69 (2021). MSC: 14B05 14J17 13H10 14C17 14J30 14J35 14J40 14L30 14M25 52B20 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Komatsu, T. Asymmetric circular graph with Hosoya index and negative continued fractions. (English) Zbl 1484.05052 Carpathian Math. Publ. 13, No. 3, 608-618 (2021). MSC: 05C09 05C92 11B39 11A55 92E10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bonanno, Claudio; Del Vigna, Alessio Representation and coding of rational pairs on a triangular tree and Diophantine approximation in \(\mathbb R^2\). (English) Zbl 1495.11038 Acta Arith. 200, No. 4, 389-427 (2021). Reviewer: Thomas B. Ward (Newcastle) MSC: 11B57 11J70 37A44 37E30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Murru, Nadir; Terracini, Lea Simultaneous approximations to \(p\)-adic numbers and algebraic dependence via multidimensional continued fractions. (English) Zbl 1480.11089 Ramanujan J. 56, No. 1, 67-86 (2021). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 11J61 11J70 12J25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Amburg, Ilya; Garrity, Thomas Functional analysis behind a family of multidimensional continued fractions. II. (English) Zbl 1488.11108 Publ. Math. Debr. 98, No. 3-4, 259-276 (2021). Reviewer: Florin P. Boca (Urbana-Champaign) MSC: 11J70 11A55 37C30 × Cite Format Result Cite Review PDF Full Text: arXiv
German, O. N.; Tlyustangelov, I. A. Symmetries of a two-dimensional continued fraction. (English. Russian original) Zbl 1469.11232 Izv. Math. 85, No. 4, 666-680 (2021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 85, No. 4, 53-68 (2021). MSC: 11J70 11H46 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rao, Hui; Yasutomi, Shin-ichi Ergodicity for \(p\)-adic continued fraction algorithms. (English) Zbl 1476.11097 Indag. Math., New Ser. 32, No. 4, 759-776 (2021). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11J70 11K41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berthé, Valérie; Nakada, Hitoshi; Natsui, Rie; Vallée, Brigitte Analysis of generalized continued fraction algorithms over polynomials. (English) Zbl 1472.11207 Finite Fields Appl. 73, Article ID 101849, 66 p. (2021). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11J70 11K50 11K55 68W40 05A15 37A44 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Fougeron, Charles; Skripchenko, Alexandra Simplicity of spectra for certain multidimensional continued fraction algorithms. (English) Zbl 1477.11138 Monatsh. Math. 194, No. 4, 767-787 (2021). Reviewer: Jörg Neunhäuserer (Goslar) MSC: 11K55 11J70 37D25 28D05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Bonanno, Claudio; Del Vigna, Alessio; Munday, Sara A slow triangle map with a segment of indifferent fixed points and a complete tree of rational pairs. (English) Zbl 1459.37007 Monatsh. Math. 194, No. 1, 1-40 (2021). Reviewer: Thomas B. Ward (Leeds) MSC: 37A40 37A44 37E25 11K50 11A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. On the second Lyapunov exponent of some multidimensional continued fraction algorithms. (English) Zbl 1473.11012 Math. Comput. 90, No. 328, 883-905 (2021). Reviewer: Takao Komatsu (Hangzhou) MSC: 11A55 11J70 11K50 37D25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Mihailescu, Eugen; Urbański, Mariusz Skew product Smale endomorphisms over countable shifts of finite type. (English) Zbl 1452.37041 Ergodic Theory Dyn. Syst. 40, No. 11, 3105-3149 (2020). Reviewer: Hasan Akin (Gaziantep) MSC: 37D35 37A35 37A44 37B10 37B51 37C45 46G10 60B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhuravlev, V. G. The best approximation of algebraic numbers by multidimensional continued fractions. (English. Russian original) Zbl 1451.11076 J. Math. Sci., New York 249, No. 1, 32-53 (2020); translation from Zap. Nauchn. Semin. POMI 479, 52-84 (2019). MSC: 11J70 11K50 × Cite Format Result Cite Review PDF Full Text: DOI
Murru, Nadir; Terracini, Lea On the finiteness and periodicity of the \(p\)-adic Jacobi-Perron algorithm. (English) Zbl 1455.11099 Math. Comput. 89, No. 326, 2913-2930 (2020). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11J70 12J25 11J61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Illarionov, Andreĭ A. The statistical properties of 3D Klein polyhedra. (English. Russian original) Zbl 1446.11130 Sb. Math. 211, No. 5, 689-708 (2020); translation from Mat. Sb. 211, No. 5, 78-97 (2020). MSC: 11H06 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Saito, Asaki; Tamura, Jun-Ichi; Yasutomi, Shin-Ichi Multidimensional \(p\)-adic continued fraction algorithms. (English) Zbl 1451.11075 Math. Comput. 89, No. 321, 351-372 (2020). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 11J70 11J61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhuravlev, V. G. Unimodular invariance of karyon expansions of algebraic numbers in multidimensional continued fractions. (English. Russian original) Zbl 1470.11201 J. Math. Sci., New York 242, No. 4, 531-559 (2019); translation from Zap. Nauchn. Semin. POMI 469, 96-137 (2018). MSC: 11J70 11K50 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. The karyon algorithm for expansion in multidimensional continued fractions. (English. Russian original) Zbl 1440.40002 J. Math. Sci., New York 242, No. 4, 487-508 (2019); translation from Zap. Nauchn. Semin. POMI 469, 32-63 (2018). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 40A15 11J70 11A55 11B57 11K50 11Y65 × Cite Format Result Cite Review PDF Full Text: DOI
Dmytryshyn, R. I. On some of convergence domains of multidimensional S-fractions with independent variables. (English) Zbl 1423.32004 Carpathian Math. Publ. 11, No. 1, 54-58 (2019). MSC: 32A17 30B70 40A15 × Cite Format Result Cite Review PDF Full Text: DOI
Murru, Nadir; Terracini, Lea On \(p\)-adic multidimensional continued fractions. (English) Zbl 1435.11092 Math. Comput. 88, No. 320, 2913-2934 (2019). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 12J25 11J61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Lennerstad, Håkan The \(n\)-dimensional Stern-Brocot tree. (English) Zbl 1450.11069 Int. J. Number Theory 15, No. 6, 1219-1236 (2019). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 11B57 11B37 05C50 × Cite Format Result Cite Review PDF Full Text: DOI Link
Bruin, Henk; Fokkink, Robbert; Kraaikamp, Cor Erratum to: “The convergence of the generalised Selmer algorithm”. (English) Zbl 1440.11145 Isr. J. Math. 231, No. 1, 505 (2019). MSC: 11K50 11K55 37A25 28D05 × Cite Format Result Cite Review PDF Full Text: DOI
Mundici, Daniele Triangles in Diophantine approximation. (English) Zbl 1459.11018 J. Number Theory 201, 176-189 (2019). MSC: 11A55 11B57 11Y65 11J70 11K60 14M25 22F05 37A20 37C85 40A15 × Cite Format Result Cite Review PDF Full Text: DOI
Dmytryshyn, R. I. Estimates of errors of approximations for multidimensional \(S\)-fraction with independentvariables. (Ukrainian. English summary) Zbl 1424.40015 Bukovyn. Mat. Zh. 6, No. 1-2, 56-59 (2018). MSC: 40A15 30B70 × Cite Format Result Cite Review PDF Full Text: Link
Karpenkov, Oleg Open problems on configuration spaces of tensegrities. (English) Zbl 1402.52025 Arnold Math. J. 4, No. 1, 19-25 (2018). MSC: 52C25 05C62 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. Localized Pisot matrices and joint approximations of algebraic numbers. (English. Russian original) Zbl 1420.11099 J. Math. Sci., New York 234, No. 5, 659-679 (2018); translation from Zap. Nauchn. Semin. POMI 458, 104-134 (2017). MSC: 11J13 11K50 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. Linear-fractional invariance of the simplex-module algorithm for expanding algebraic numbers in multidimensional continued fractions. (English. Russian original) Zbl 1420.11108 J. Math. Sci., New York 234, No. 5, 640-658 (2018); translation from Zap. Nauchn. Semin. POMI 458, 77-103 (2017). MSC: 11K50 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. Linear-fractional invariance of multidimensional continued fractions. (English. Russian original) Zbl 1411.11069 J. Math. Sci., New York 234, No. 5, 616-639 (2018); translation from Zap. Nauchn. Semin. POMI 458, 42-76 (2017). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11J70 11B57 11J68 11K50 11Y65 × Cite Format Result Cite Review PDF Full Text: DOI
Garrity, Thomas; Mcdonald, Peter Generalizing the Minkowski question mark function to a family of multidimensional continued fractions. (English) Zbl 1445.11060 Int. J. Number Theory 14, No. 9, 2473-2516 (2018). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 11K60 26A30 26B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bodnar, O. S.; Dmytryshyn, R. I. On the convergence of multidimensional \(S\)-fractions with independent variables. (English) Zbl 1407.40006 Carpathian Math. Publ. 10, No. 1, 58-64 (2018). MSC: 40A15 30B70 × Cite Format Result Cite Review PDF Full Text: DOI
Illarionov, Andrei A. Distribution of facets of higher-dimensional Klein polyhedra. (English. Russian original) Zbl 1417.11133 Sb. Math. 209, No. 1, 56-70 (2018); translation from Mat. Sb. 209, No. 1, 58-73 (2018). MSC: 11J70 11K50 52C07 11H16 × Cite Format Result Cite Review PDF Full Text: DOI
Dmytryshyn, R. I. Convergence of some branched continued fractions with independent variables. (English) Zbl 1433.11003 Mat. Stud. 47, No. 2, 150-159 (2017). MSC: 11A55 11J70 30B70 40A15 × Cite Format Result Cite Review PDF Full Text: DOI
Dmytryshyn, R. I. On convergence of multidimensional \(J\)-fraction with nonequivalent variables. (Ukrainian. English summary) Zbl 1399.30015 Bukovyn. Mat. Zh. 5, No. 3-4, 71-76 (2017). MSC: 30B70 × Cite Format Result Cite Review PDF
Dmytryshyn, R. I. On the convergence criterion for branched continued fractions with independent variables. (English) Zbl 1390.11019 Carpathian Math. Publ. 9, No. 2, 120-127 (2017). MSC: 11A55 11J70 30B70 40A15 × Cite Format Result Cite Review PDF Full Text: DOI
Murru, Nadir Linear recurrence sequences and periodicity of multidimensional continued fractions. (English) Zbl 1432.11080 Ramanujan J. 44, No. 1, 115-124 (2017). MSC: 11J70 11B37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Zhuravlev, V. G. Simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions. (English. Russian original) Zbl 1412.11084 J. Math. Sci., New York 225, No. 6, 924-949 (2017); translation from Zap. Nauchn. Semin. POMI 449, 130-167 (2016). MSC: 11K16 11J70 11K55 11Y40 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. Periodic karyon expansions of algebraic units in multidimensional continued fractions. (English. Russian original) Zbl 1416.11127 J. Math. Sci., New York 225, No. 6, 893-923 (2017); translation from Zap. Nauchn. Semin. POMI 449, 84-129 (2016). MSC: 11J70 11K55 11K16 × Cite Format Result Cite Review PDF Full Text: DOI
Amburg, Ilya; Dasaratha, Krishna; Flapan, Laure; Garrity, Thomas; Lee, Chansoo; Mihaila, Cornelia; Neumann-Chun, Nicholas; Peluse, Sarah; Stoffregen, Matthew Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences. (English) Zbl 1420.11054 J. Integer Seq. 20, No. 1, Article 17.1.7, 43 p. (2017). MSC: 11B83 11A55 11J70 40A99 × Cite Format Result Cite Review PDF Full Text: arXiv EMIS
Moshchevitin, Nikolay On a question of N. Chevallier related to simultaneous Diophantine approximation. (Sur une question de N. Chevallier liée à l’approximation diophantienne simultanée.) (French. English summary) Zbl 1415.11093 J. Théor. Nombres Bordx. 28, No. 3, 583-595 (2016). MSC: 11J13 11J70 11K60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dmytryshyn, R. I. A multidimensional generalization of the Rutishauser qd-algorithm. (English) Zbl 1401.40004 Carpathian Math. Publ. 8, No. 2, 230-238 (2016). MSC: 40A15 30B10 30B70 65B10 × Cite Format Result Cite Review PDF Full Text: DOI
Cheung, Yitwah; Chevallier, Nicolas Hausdorff dimension of singular vectors. (English) Zbl 1358.11078 Duke Math. J. 165, No. 12, 2273-2329 (2016). Reviewer: Mumtaz Hussain (Bendigo) MSC: 11J13 11K55 11K60 37A17 × Cite Format Result Cite Review PDF Full Text: DOI Euclid Link
Makarov, V. L.; Demkiv, I. I. Generalization of the Thiele fraction. (Ukrainian. English summary) Zbl 1363.41006 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2016, No. 2, 17-24 (2016). MSC: 41A05 30B70 65D05 41A63 × Cite Format Result Cite Review PDF Full Text: DOI
Borodina, E. B. An algorithm for constructing multidimensional continued fractions and linear dependence of numbers. (English. Russian original) Zbl 1370.11081 Math. Notes 99, No. 1, 37-45 (2016); translation from Mat. Zametki 99, No. 1, 26-34 (2016). MSC: 11J70 11Y16 × Cite Format Result Cite Review PDF Full Text: DOI
Lachaud, Jacques-Olivier; Provençal, Xavier; Roussillon, Tristan An output-sensitive algorithm to compute the normal vector of a digital plane. (English) Zbl 1338.68265 Theor. Comput. Sci. 624, 73-88 (2016). MSC: 68U05 × Cite Format Result Cite Review PDF Full Text: DOI
Illarionov, A. A. The distribution of integer lengths of Klein polyhedra edges. (Russian. English summary) Zbl 1386.11021 Dal’nevost. Mat. Zh. 15, No. 2, 214-221 (2015). MSC: 11A55 11H06 × Cite Format Result Cite Review PDF Full Text: MNR
Bruin, Henk; Fokkink, Robbert; Kraaikamp, Cor The convergence of the generalised Selmer algorithm. (English) Zbl 1332.11072 Isr. J. Math. 209, Part 2, 803-823 (2015); erratum ibid. 231, No. 1, 505 (2019). Reviewer: Enrico Zoli (Firenze) MSC: 11K50 11K55 37A25 28D05 × Cite Format Result Cite Review PDF Full Text: DOI
Illarionov, A. A. Some properties of three-dimensional Klein polyhedra. (English. Russian original) Zbl 1327.11044 Sb. Math. 206, No. 4, 510-539 (2015); translation from Mat. Sb. 206, No. 4, 35-66 (2015). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11H06 11J70 52C07 × Cite Format Result Cite Review PDF Full Text: DOI
Berthé, V.; Labbé, S. Factor complexity of \(S\)-adic words generated by the Arnoux-Rauzy-Poincaré algorithm. (English) Zbl 1310.68170 Adv. Appl. Math. 63, 90-130 (2015). Reviewer: Wolfgang Steiner (Sydney) MSC: 68R15 37B10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dasaratha, Krishna; Flapan, Laure; Garrity, Thomas; Lee, Chansoo; Mihaila, Cornelia; Neumann-Chun, Nicholas; Peluse, Sarah; Stoffregen, Matthew A generalized family of multidimensional continued fractions: TRIP maps. (English) Zbl 1378.11074 Int. J. Number Theory 10, No. 8, 2151-2186 (2014). MSC: 11J70 11A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Vodolagin, M. Yu. Moments for the multidimensional Mönkemeyer algorithm. (English. Russian original) Zbl 1325.11068 St. Petersbg. Math. J. 25, No. 4, 533-545 (2014); translation from Algebra Anal. 25, No. 4, 28-46 (2013). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Cui, Rongrong; Gu, Chuanqing A method of triple Newton-Thiele type rational interpolation. (Chinese. English summary) Zbl 1313.65015 J. Shanghai Univ., Nat. Sci. 20, No. 1, 107-113 (2014). MSC: 65D05 41A05 41A20 11J70 41A63 × Cite Format Result Cite Review PDF Full Text: DOI
Dasaratha, Krishna; Flapan, Laure; Garrity, Thomas; Lee, Chansoo; Mihaila, Cornelia; Neumann-Chun, Nicholas; Peluse, Sarah; Stoffregen, Matthew Cubic irrationals and periodicity via a family of multi-dimensional continued fraction algorithms. (English) Zbl 1305.11060 Monatsh. Math. 174, No. 4, 549-566 (2014). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J70 11A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Illarionov, A. A. A multidimensional generalization of Heilbronn’s theorem on the average length of a finite continued fraction. (English. Russian original) Zbl 1298.11064 Sb. Math. 205, No. 3, 419-431 (2014); translation from Mat. Sb. 205, No. 3, 119-132 (2014). Reviewer: Steven T. Dougherty (Scranton) MSC: 11H06 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Beukers, Frits Geodesic continued fractions and LLL. (English) Zbl 1369.11050 Indag. Math., New Ser. 25, No. 4, 632-645 (2014). MSC: 11J70 11J13 11Y65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chevallier, Nicolas Stepped hyperplane and extension of the three distance theorem. (English) Zbl 1305.11058 Assani, Idris (ed.), Ergodic theory and dynamical systems. Proceedings of the ergodic theory workshops at University of North Carolina at Chapel Hill, NC, USA, March 17–21, 2011 and March 22–25, 2012. Berlin: de Gruyter (ISBN 978-3-11-029813-0/hbk; 978-3-11-029820-8/ebook). De Gruyter Proceedings in Mathematics, 81-92 (2014). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J70 11J71 11H99 × Cite Format Result Cite Review PDF
Håstad, J.; Just, B.; Lagarias, J. C.; Schnorr, C. P. Erratum: “Polynomial time algorithms for finding integer relations among real numbers”. (English) Zbl 1290.11106 SIAM J. Comput. 43, No. 1, 254 (2014). MSC: 11J70 11H06 11H55 11Y16 11Y65 68Q25 × Cite Format Result Cite Review PDF Full Text: DOI
German, O. N. Badly approximable matrices and Diophantine exponents. (Russian. English summary) Zbl 1423.11120 Chebyshevskiĭ Sb. 14, No. 4(48), 38-79 (2013); translation in Dokl. Math. 106, Suppl. 2, S201-S220 (2022). MSC: 11J13 11J70 × Cite Format Result Cite Review PDF Full Text: MNR
Chevallier, Nicolas Best simultaneous Diophantine approximations and multidimensional continued fraction expansions. (English) Zbl 1305.11059 Mosc. J. Comb. Number Theory 3, No. 1, 3-56 (2013). Reviewer: Ahmet Tekcan (Bursa) MSC: 11J70 11J13 × Cite Format Result Cite Review PDF
Melançon, Guy; Reutenauer, Christophe On a class of Lyndon words extending Christoffel words and related to a multidimensional continued fraction algorithm. (English) Zbl 1298.68206 J. Integer Seq. 16, No. 9, Article 13.9.7, 30 p. (2013). Reviewer: Tobias Mühlenbruch (Hagen) MSC: 68R15 11J70 × Cite Format Result Cite Review PDF Full Text: EMIS
Garrity, Thomas A multidimensional continued fraction generalization of Stern’s diatomic sequence. (English) Zbl 1342.11038 J. Integer Seq. 16, No. 7, Article 13.7.7, 24 p. (2013). MSC: 11B83 11A55 11J70 40A15 × Cite Format Result Cite Review PDF Full Text: arXiv EMIS
Berthé, Valérie; Lacasse, Annie; Paquin, Geneviève; Provençal, Xavier A study of Jacobi-Perron boundary words for the generation of discrete planes. (English) Zbl 1296.68113 Theor. Comput. Sci. 502, 118-142 (2013). MSC: 68R15 52C35 × Cite Format Result Cite Review PDF Full Text: DOI
Illarionov, A. A. Cylindrical minima of integral lattices. (English. Russian original) Zbl 1273.11103 St. Petersbg. Math. J. 24, No. 2, 301-312 (2013); translation from Algebra Anal. 24, No. 2, 154-170 (2012). MSC: 11H06 11H50 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Karpenkov, Oleg Geometry of continued fractions. (English) Zbl 1297.11002 Algorithms and Computation in Mathematics 26. Berlin: Springer (ISBN 978-3-642-39367-9/hbk; 978-3-642-39368-6/ebook). xvii, 405 p. (2013). Reviewer: Lenny Fukshansky (Claremont) MSC: 11-02 11J70 11A55 11H55 11K50 30B70 40A15 × Cite Format Result Cite Review PDF Full Text: DOI
Karpenkov, Oleg Multidimensional Gauss reduction theory for conjugacy classes of \(\mathrm{SL}(n,\mathbb Z)\). (English. French summary) Zbl 1273.11111 J. Théor. Nombres Bordx. 25, No. 1, 99-109 (2013). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11J70 11A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Illarionov, A. A. On statistical properties of local minima of integer lattices. (Russian. English summary) Zbl 1292.11081 Dal’nevost. Mat. Zh. 12, No. 2, 201-230 (2012). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 11H16 × Cite Format Result Cite Review PDF
Miernowski, Tomasz; Nogueira, Arnaldo Absorbing sets of homogeneous subtractive algorithms. (English) Zbl 1337.11052 Monatsh. Math. 167, No. 3-4, 547-569 (2012). MSC: 11K50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Illarionov, A. A. The average number of relative minima of three-dimensional integer lattices of a given determinant. (English. Russian original) Zbl 1264.11055 Izv. Math. 76, No. 3, 535-562 (2012); translation from Izv. Ross. Akad. Nauk, Ser. Mat 76, No. 3, 111-138 (2012). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11H06 11H56 11H60 × Cite Format Result Cite Review PDF Full Text: DOI
Illarionov, A. A. Average number of local minima for three-dimensional integral lattices. (English. Russian original) Zbl 1261.11048 St. Petersbg. Math. J. 23, No. 3, 551-570 (2012); translation from Algebra Anal. 23, No. 3, 189-215 (2011). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11H06 11H50 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Schweiger, Fritz Variations of the Poincaré map. (English) Zbl 1333.11080 Integers 12, No. 2, 167-178 (2012) and 11, A56, 12 p. (2011). MSC: 11K55 37A44 × Cite Format Result Cite Review PDF Full Text: DOI
Kops, J. Christopher Selmer’s multiplicative algorithm. (English) Zbl 1241.11077 Integers 12, No. 1, 1-20 (2012); 11, A45, 20 p. (2011). MSC: 11J70 11K55 11J13 28D05 × Cite Format Result Cite Review PDF Full Text: DOI EMIS
Schweiger, F. A 2-dimensional algorithm related to the Farey-Brocot sequence. (English) Zbl 1295.11085 Int. J. Number Theory 8, No. 1, 149-160 (2012). MSC: 11K55 11J70 28D99 37A45 × Cite Format Result Cite Review PDF Full Text: DOI
Berthé, Valérie; Labbé, Sébastien Uniformly balanced words with linear complexity and prescribed letter frequencies. (English) Zbl 1331.68161 Ambrož, Petr (ed.) et al., Proceedings of the 8th international conference, Words 2011, Prague, Czech Republic, September, 12–16, 2011. Sydney: NICTA. Electronic Proceedings in Theoretical Computer Science 63, 44-52 (2011). MSC: 68R15 11Y65 68U05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EMIS
Dmytryshyn, Roman About some regions of convergence of a multidimensional \(J\)-fraction with independent variables. (Ukrainian. English summary) Zbl 1265.40011 Mat. Visn. Nauk. Tov. Im. Shevchenka 8, 69-77 (2011). MSC: 40A15 30B70 × Cite Format Result Cite Review PDF
Fokkink, R.; Kraaikamp, C.; Nakada, H. On Schweiger’s problems on fully subtractive algorithms. (English) Zbl 1273.11119 Isr. J. Math. 186, 285-296 (2011). Reviewer: Marius Iosifescu (Bucureşti) MSC: 11K50 37A45 × Cite Format Result Cite Review PDF Full Text: DOI
Illarionov, Andrey On the asymptotic distribution of integer matrices. (English) Zbl 1284.11100 Mosc. J. Comb. Number Theory 1, No. 4, 13-57 (2011). Reviewer: Roland Quême (Brax) MSC: 11J71 11J70 × Cite Format Result Cite Review PDF
Illarionov, A. A.; Slinkin, D. A. The average number of vertices of Klein polyhedra for integer lattices. (Russian. English summary) Zbl 1270.11065 Dal’nevost. Mat. Zh. 11, No. 1, 48-55 (2011). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11H06 11H50 11J70 × Cite Format Result Cite Review PDF Full Text: MNR
Illarionov, A. A. On cylindrical minima of three-dimensional lattices. (Russian. English summary) Zbl 1261.11049 Dal’nevost. Mat. Zh. 11, No. 1, 37-47 (2011). MSC: 11H06 11H50 11J70 × Cite Format Result Cite Review PDF Full Text: MNR
Maloney, Gregory R. Dimension groups and multidimensional continued fractions. (English) Zbl 1225.46050 C. R. Math. Acad. Sci., Soc. R. Can. 33, No. 1, 11-20 (2011). Reviewer: Igor V. Nikolaev (Ottawa) MSC: 46L80 46L35 46L85 × Cite Format Result Cite Review PDF
Wang, Quanlong On simultaneous rational approximation to \( (\alpha,\alpha^2)^{\text{T}}\) with \(\alpha^3+kd \alpha-d=0\). (Chinese. English summary) Zbl 1240.11074 J. Jiangxi Norm. Univ., Nat. Sci. Ed. 34, No. 6, 576-581 (2010). MSC: 11J70 11J13 × Cite Format Result Cite Review PDF
Zhang, Yuwu; Zhao, Qianjin; Tang, Ruzhong A novel bivariate blending rational interpolation with high accuracy. (Chinese. English summary) Zbl 1240.65031 J. Hefei Univ. Technol., Nat. Sci. 33, No. 12, 1908-1911 (2010). MSC: 65D05 41A05 41A20 41A63 11A55 × Cite Format Result Cite Review PDF Full Text: DOI
Tang, Shuo; Yang, Mingjuan Matrix algorithm to bivariate Newton associated continued fraction interpolation. (Chinese. English summary) Zbl 1240.65028 J. Hefei Univ. Technol., Nat. Sci. 33, No. 8, 1260-1263 (2010). MSC: 65D05 41A05 41A63 11A55 × Cite Format Result Cite Review PDF Full Text: DOI
Moshchevitin, N. G. Khintchine’s singular Diophantine systems and their applications. (English. Russian original) Zbl 1225.11094 Russ. Math. Surv. 65, No. 3, 433-511 (2010); translation from Uspekhi Mat. Nauk. 65, No. 3, 43-126 (2010). Reviewer: Artūras Dubickas (Vilnius) MSC: 11J13 11J83 37A45 11-02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ferenczi, Sébastien; Zamboni, Luca Q. Structure of \(K\)-interval exchange transformations: induction, trajectories, and distance theorems. (English) Zbl 1225.37003 J. Anal. Math. 112, 289-328 (2010). Reviewer: William J. Satzer jun. (St. Paul) MSC: 37A05 37B10 68R15 × Cite Format Result Cite Review PDF Full Text: DOI
Schweiger, Fritz Volume as a measure of approximation for the Jacobi-Perron algorithm. (English) Zbl 1197.11079 Integers 10, No. 1, 65-71, A6 (2010). Reviewer: Thomas Schmidt (Corvallis) MSC: 11J70 11J06 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Berthé, Valérie Discrete geometry and numeration. (English) Zbl 1480.37022 Actes Rencontres C.I.R.M. 1, No. 1, 17-22 (2009). MSC: 37B10 37B51 37B52 37E15 11A55 52C99 × Cite Format Result Cite Review PDF Full Text: DOI Link
Broise-Alamichel, Anne On the characteristic exponents of the Jacobi-Perron algorithm. (English) Zbl 1303.11077 Bugeaud, Yann (ed.) et al., Dynamical systems and Diophantine approximation. Paris: Société Mathématique de France (ISBN 978-2-85629-303-4/pbk). Séminaires et Congrès 19, 151-171 (2009). MSC: 11J70 11K55 11J13 × Cite Format Result Cite Review PDF
Dai, Zongduo; Wang, Kunpeng; Ye, Dingfeng Characterization of multi-continued fractions for multi-formal Laurent series. (English) Zbl 1283.11104 Dong, Chongying (ed.) et al., Recent developments in algebra and related areas. Papers of the international conference on algebra and related areas, Tsinghua University, Beijing, China, August 18–20, 2007. Dedicated to Zhexian Wan in honor of his 80th birthday. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-135-3/pbk). Advanced Lectures in Mathematics (ALM) 8, 59-80 (2009). Reviewer: Olaf Ninnemann (Berlin) MSC: 11J70 11J61 11A55 11B37 × Cite Format Result Cite Review PDF