On the volume and the number of lattice points of some semialgebraic sets
2015 ◽
Vol 26
(10)
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pp. 1550078
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Keyword(s):
Let f = (f1,…,fm) : ℝn→ ℝmbe a polynomial map; we consider the set Gf(r) = {x ∈ ℝn: |fi(x)| ≤ r, i = 1,…,m}. We show that if f satisfies the Mikhailov–Gindikin condition then:(i) Volume Gf(r) ≍ rθ( ln r)n-k-1,(ii) Cardinal [Formula: see text], as r → ∞,where the exponents θ, k, θ′, k′ are determined explicitly in terms of the Newton polyhedra of f. Moreover, the polynomial maps satisfying the Mikhailov–Gindikin condition form an open subset of the set of polynomial maps having the same Newton polyhedron.
2002 ◽
Vol 39
(3-4)
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pp. 361-367
Keyword(s):
2016 ◽
Vol 16
(08)
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pp. 1750141
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2009 ◽
Vol 19
(02)
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pp. 531-543
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Keyword(s):
Keyword(s):
2010 ◽
Vol 147
(1)
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pp. 332-334
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Keyword(s):
Keyword(s):