On the volume and the number of lattice points of some semialgebraic sets

DOI10.1142/S0129167X15500780zbMath1386.14198arXiv1502.06091OpenAlexW2963869331MaRDI QIDQ3450727

Ha Huy Vui, Tran Gia Loc

Publication date: 6 November 2015

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.06091

zbMATH Keywords

lattice pointsNewton polyhedronsublevel setthe Mikhailov-Gindikin condition

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Linear programming (90C05) Singularities in algebraic geometry (14B05) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Semialgebraic sets and related spaces (14P10) Lattice points in specified regions (11P21)

Related Items (3)

Integrability at infinity of negative powers of polynomials in the plane and its application to convergence of Dirichlet series ⋮ Newton polygon and distribution of integer points in sublevel sets ⋮ Łojasiewicz gradient inequalities for polynomial functions and some applications

Cites Work

• Stability of oscillatory integral asymptotics in two dimensions
• Resolution of singularities in two dimensions and the stability of integrals
• Uniform estimates of oscillatory integrals with parabolic or hyperbolic phase
• Newton polyhedra and estimation of oscillating integrals
• The Newton polyhedron and oscillatory integral operators
• Oscillating integrals and Newton polyhedra
• Newton's Polyhedron and Weyl's Formula for the Spectrum of the Schrödinger Operator with Polynomial Potential
• Radon transforms and finite type conditions
• Lectures on Polytopes
• Convex Polytopes
• Multilinear level set operators, oscillatory integral operators, and Newton polyhedra

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