caa a22 4500 46317786X CHVBK 20180406164830.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s11139-006-9001-9 doi (NATIONALLICENCE)springer-10.1007/s11139-006-9001-9 Wakabayashi Isao Faculty of Science and Technology, Seikei University, Kichijoji Kitamachi, Musashino-shi, 180-8633, Tokyo, Japan aut Number of solutions for cubic Thue equations with automorphisms [Elektronische Daten] [Isao Wakabayashi] Let $$F(X,Y)\in {\boldmath Z} [X,Y]$$ be an irreducible cubic form with positive discriminant, and with non-trivial automorphisms. We show that the Thue equation F(x,y) = 1 has at most three integer solutions except for a few known cases. For the proof, we use an explicitly expressed cubic form which is equivalent to F. To obtain an upper bound for the size of solutions, we use the Padé approximation method developed in our former work. To obtain a lower bound for the size of solutions, we use a result of R. Okazaki on gaps between solutions, which is obtained by geometric consideration. Springer Science + Business Media, LLC, 2006 Cubic Thue equation nationallicence Automorphism of forms nationallicence Simplest cubic nationallicence The Ramanujan Journal Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 14/1(2007-08-01), 131-154 1382-4090 14:1<131 2007 14 11139 https://doi.org/10.1007/s11139-006-9001-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-9001-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wakabayashi Isao Faculty of Science and Technology, Seikei University, Kichijoji Kitamachi, Musashino-shi, 180-8633, Tokyo, Japan aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 14/1(2007-08-01), 131-154 1382-4090 14:1<131 2007 14 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer