Zero order estimates for functions satisfying generalized functional equations of Mahler type

 Access to full text

 Full (PDF)

1. [B1] P.-G. Becker-Landeck, Maße für algebraische Unabhängigkeit nach einer Methode von Mahler, Acta Arith. 50 (1988), 279-293. 
2. [B2] P.-G. Becker, Effective measures for algebraic independence of the values of Mahler type functions, Acta Arith. 58 (1991), 239-250. 
3. [B3] P.-G. Becker, Algebraic independence of the values of certain series by Mahler's method, Monatsh. Math. 114 (1992), 183-198. Zbl0764.11029
4. [B4] P.-G. Becker, Transcendence of the values of functions satisfying generalized Mahler type functional equations, J. Reine Angew. Math. 440 (1993), 111-128. Zbl0770.11037
5. [B5] P.-G. Becker, Transcendence measures for the values of generalized Mahler functions in arbitrary characteristic, Publ. Math. Debrecen 45 (1994), 269-282. Zbl0815.11037
6. [K] K. K. Kubota, Linear functional equations and algebraic independence, in: Transcendence Theory: Advances and Applications, A. Baker and D. W. Masser (eds.), Academic Press, New York, 1977, 227-229. 
7. [L] J. H. Loxton, Automata and transcendence, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge Univ. Press, Cambridge, 1988, 215-228. 
8. [LP] J. H. Loxton and A. J. van der Poorten, Transcendence and algebraic independence by a method of Mahler, in: Transcendence Theory: Advances and Applications, A. Baker and D. W. Masser (eds.), Academic Press, New York, 1977, 211-226. Zbl0378.10020
9. [Ne1] Yu. V. Nesterenko, Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 253-284 (in Russian); English transl.: Math. USSR-Izv. 11 (1977), 239-270. 
10. [Ne2] Yu. V. Nesterenko, On algebraic independence of algebraic powers of algebraic numbers, Mat. Sb. 123 (165) (1984), 435-459 (in Russian); English transl.: Math. USSR-Sb. 51 (1985), 429-454. Zbl0549.10023
11. [Ne3] Yu. V. Nesterenko, On a measure of the algebraic independence of the values of certain functions, Mat. Sb. 128 (170) (1985), 545-568 (in Russian); English transl.: Math. USSR-Sb. 56 (1987), 545-567. Zbl0603.10033
12. [Ni1] K. Nishioka, On an estimate for the orders of zeros of Mahler type functions, Acta Arith. 56 (1990), 249-256. 
13. [Ni2] K. Nishioka, Algebraic independence measures of the values of Mahler functions, J. Reine Angew. Math. 420 (1991), 203-214. Zbl0736.11034
14. [NT] K. Nishioka and T. Töpfer, Transcendence measures and nonlinear functional equations of Mahler type, Arch. Math. (Basel) 57 (1991), 370-378. Zbl0704.11014
15. [P1] P. Philippon, Critères pour l'indépendance algébrique, Inst. Hautes Etudes Sci. Publ. Math. 64 (1986), 5-52. 
16. [P2] P. Philippon, Critères pour l'indépendance algébrique dans les anneaux diophantiens, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), 511-515. Zbl0781.13011
17. [T1] T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions, J. Number Theory 49 (1994), 1-26. Zbl0813.11043
18. [T2] T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions II, Compositio Math. 95 (1995), 323-342. Zbl0839.11028
19. [T3] T. Töpfer, Algebraic independence of the values of generalized Mahler functions, Acta Arith. 70 (1995), 161-181. Zbl0815.11038
20. [W] N. C. Wass, Algebraic independence of the values at algebraic points of a class of functions considered by Mahler, Dissertationes Math. 303 (1990). Zbl0707.11050