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- Title
Dilation of Newton Polytope and p-adic Estimate.
- Authors
Wei Cao
- Abstract
Let f( X) be a polynomial in n variables over the finite field $\mathbb{F}_{q}$. Its Newton polytope Δ( f) is the convex closure in ℝ of the origin and the exponent vectors (viewed as points in ℝ) of monomials in f( X). The minimal dilation of Δ( f) such that it contains at least one lattice point of $\mathbb{Z}_{>0}^{n}$ plays a vital pole in the p-adic estimate of the number of zeros of f( X) in $\mathbb{F}_{q}$. Using this fact, we obtain several tight and computational bounds for the dilation which unify and improve a number of previous results in this direction.
- Subjects
BLOWING up (Algebraic geometry); CONVEX polytopes; NORMAL basis theorem; P-adic fields; P-adic logarithms
- Publication
Discrete & Computational Geometry, 2011, Vol 45, Issue 3, p522
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-010-9244-5