Algebraic independence of the generating functions of Stern’s sequence and of its twist
Peter Bundschuh[1]; Keijo Väänänen[2]
- [1] Mathematisches Institut Universität zu Köln Weyertal 86-90 50931 Köln, Germany
- [2] Department of Mathematical Sciences University of Oulu P. O. Box 3000 90014 Oulu, Finland
Journal de Théorie des Nombres de Bordeaux (2013)
- Volume: 25, Issue: 1, page 43-57
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topReferences
top- B. Adamczewski and T. Rivoal, Irrationality measures for some automatic real numbers. Math. Proc. Cambridge Phil. Soc. 147 (2009), 659–678. Zbl1205.11080MR2557148
- J.-P. Allouche, On the Stern sequence and its twisted version. Integers 12 (2012), A58. Zbl1283.11026MR2955582
- M. Amou, Algebraic independence of the values of certain functions at a transcendental number. Acta Arith. 59 (1991), 71–82. Zbl0735.11031MR1133238
- R. Bacher, Twisting the Stern sequence. Preprint, 2010, available at http://arxiv.org/abs/1005.5627
- Y. Bugeaud, On the rational approximation to the Thue-Morse-Mahler numbers. Ann. Inst. Fourier (Grenoble) 61 (2011), 2065–2076. Zbl1271.11074MR2961848
- P. Bundschuh, Transcendence and algebraic independence of series related to Stern’s squence. Int. J. Number Theory 8 (2012), 361–376. Zbl1288.11070MR2890484
- F. Carlson, Über Potenzreihen mit ganzen Koeffizienten. Math. Z. 9 (1921), 1–13. Zbl48.1208.02MR1544447
- M. Coons, The transcendence of series related to Stern’s diatomic sequence. Int. J. Number Theory 6 (2010), 211–217. Zbl1250.11015MR2641723
- P. Corvaja and U. Zannier, Some new applications of the subspace theorem. Compos. Math. 131 (2002), 319–340. Zbl1010.11038MR1905026
- K. K. Kubota, On the algebraic independence of holomorphic solutions of certain functional equations and their values. Math. Ann. 227 (1977), 9–50. Zbl0359.10030MR498423
- K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen. Math. Ann. 101 (1929), 342–366. Zbl55.0115.01MR1512537
- Ke. Nishioka, A note on differentially algebraic solutions of first order linear difference equations. Aequationes Math. 27 (1984), 32–48. Zbl0542.12012MR758857
- Ku. Nishioka, New approach in Mahler’s method. J. Reine Angew. Math. 407 (1990), 202–219. Zbl0694.10035MR1048535
- Ku. Nishioka, Mahler Functions and Transcendence, Lecture Notes in Math. 1631. Springer, Berlin, 1996. Zbl0876.11034MR1439966
- M. A. Stern, Über eine zahlentheoretische Funktion. J. Reine Angew. Math. 55 (1858), 193–220.