caa a22 4500 47574134X CHVBK 20180406123500.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/BF02675796 doi (NATIONALLICENCE)springer-10.1007/BF02675796 Parusnikov V. M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, USSR aut Klein polyhedra for the fourth extremal cubic form [Elektronische Daten] [V. Parusnikov] Davenport and Swinnerton-Dyer found the first 19 extremal ternary cubic formsg i; they have the same meaning as the familiar Markov forms in the binary quadratic case. The Klein polyhedra for the formsg 1,g 2,g 3 were recently computed by Bryuno and Parusnikov. The same authors computed the convergents for certain matrix generalizations of the continued fraction algorithm and studied their arrangement with respect to the Klein polyhedra. Here we consider similar problems for the fourth formg 4. Namely, the Klein polyhedra forg 4 and the conjugate formg 4* are computed. They turn out to be essentially different. Their periods and fundamental domains are found. The matrix algorithm expansions of the vectors of these forms are calculated. Kluwer Academic/Plenum Publishers, 2000 ternary cubic forms nationallicence convergents of continued fractions nationallicence Klein polyhedra nationallicence continued fractions nationallicence the fourth extremal form nationallicence Z-modules nationallicence lattices nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 87-102 0001-4346 67:1<87 2000 67 11006 https://doi.org/10.1007/BF02675796 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02675796 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Parusnikov V. M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 87-102 0001-4346 67:1<87 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer