Roth’s theorem with moving targets. (English) Zbl 0877.11041

Vojta, Paul

Int. Math. Res. Not. 1996, No. 3, 109-114 (1996).

The author applies his ‘dictionary’ translating between diophantine approximation and value distribution theory (see Lect. Notes Math. 1239, Springer–Verlag, Berlin (1987; Zbl 0609.14011) to translate Osgood’s generalisation of the second main theorem of Nevanlinna theory [C. F. Osgood, J. Number Theory 21, 347-389 (1985; Zbl 0575.10032)]) into ‘Roth’s theorem with moving targets’. The reviewer notes with gratification that the author suggests that E. Bombieri and A. J. van der Poorten once proved a very particular case of this result [J. Austr. Math. Soc., Ser. A. 45, 233-248 (1988; Zbl 0664.10017)], but nonetheless will not essay here to explain just what constitutes targets moving.

Reviewer: A.J.van der Poorten (North Ryde)

MSC:

11J68	Approximation to algebraic numbers
30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Keywords:

Roth’s theorem; diophantine approximation; value distribution theory; Nevanlinna theory; moving targets

Citations:

Zbl 0609.14011; Zbl 0575.10032; Zbl 0664.10017