Diophantine inequalities and quasi-algebraically closed fields

作者:Spencer Craig V*; Wooley Trevor D
来源:Israel Journal of Mathematics, 2012, 191(2): 721-738.
DOI:10.1007/s11856-012-0004-5

摘要

Consider a form g(x (1),...,x (s) ) of degree d, having coefficients in the completion of the field of fractions associated to the finite field . We establish that whenever s %26gt; d (2), then the form g takes arbitrarily small values for non-zero arguments . We provide related results for problems involving distribution modulo , and analogous conclusions for quasi-algebraically closed fields in general.

  • 出版日期2012-10