Diophantine inequalities and quasi-algebraically closed fields |
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| Authors: | Craig V. Spencer Trevor D. Wooley |
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| Affiliation: | 1.Department of Mathematics,Kansas State University,Manhattan,USA;2.School of Mathematics,University of Bristol University Walk,Bristol,UK |
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| Abstract: | 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 > 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. |
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