On zeros of multilinear polynomials
نویسندگان
چکیده
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For system such satisfying certain technical conditions we prove existence search bounds for simultaneous zeros with respect to height. single polynomial, height lying outside prescribed algebraic set. also obtain case homogeneous multilinear polynomials, which are related so-called “sparse” version Siegel's lemma. Among tools develop inequalities that independent interest.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2023
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2022.10.003