论文信息 - Determinants in the Study of Thue's Method and Curves with Prescribed Singularities

Determinants in the Study of Thue's Method and Curves with Prescribed Singularities

Our investigations in the 1980's of Thue's method yielded determinants that we were only able to analyse successfully in part. We explain the context of our work, recount our experiences, mention our conjectures, and allude to a number of open questions.

[1] A. V. D. Poorten,et al. Kurt Mahler, 1903–1988 , 1991, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[2] G. M.. The Theory of Determinants in the Historical Order of Development , 1906, Nature.

[3] Paul Vojta. Siegel's theorem in the compact case , 1991 .

[4] Enrico Bombieri,et al. On Siegel's lemma , 1983 .

[5] E. Bombieri,et al. On effective measures of irrationality for and related numbers. , 1983 .

[6] Enrico Bombieri,et al. Some quantitative results related to Roth's Theorem , 1988 .

[7] G. Harcos,et al. The Institute for Advanced Study , 1933, Nature.

[8] T. Muir. The Theory of Determinants in the Historical Order of Development , 1920 .

[9] Paula B. Cohen,et al. EFFECTIVE DIOPHANTINE APPROXIMATION ON GM, II , 1997 .

[10] A. J. Poorten. Some determinants that should be better known , 1976, Journal of the Australian Mathematical Society.

[11] Eckart Viehweg,et al. Dyson's Lemma for polynomials in several variables (and the Theorem of roth) , 1984 .

[12] Paul Vojta. Dyson's lemma for products of two curves of arbitrary genus , 1989 .

[13] Enrico Bombieri,et al. On the Thue-Siegel-Dyson theorem , 1982 .