Oscillating integrals and Newton polyhedra

DOI10.1007/BF02791501zbMath1093.14006arXivmath/0405317MaRDI QIDQ2565917

Johannes Nicaise, Patrick Sargos, Jan Denef

Publication date: 28 September 2005

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405317

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Singularities in algebraic geometry (14B05) Local complex singularities (32S05) Asymptotic behavior of solutions to equations on manifolds (58K55)

Related Items (10)

On the volume and the number of lattice points of some semialgebraic sets ⋮ The asymptotic behavior of degenerate oscillatory integrals in two dimensions ⋮ Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude ⋮ Archimedean zeta functions and oscillatory integrals ⋮ Meromorphic continuations of local zeta functions and their applications to oscillating integrals ⋮ Resolution of singularities for \(C^\infty\) functions and meromorphy of local zeta functions ⋮ Uniform estimates for the Fourier transform of surface carried measures in \(\mathbb R^{3}\) and an application to Fourier restriction ⋮ Newton polyhedra and weighted oscillatory integrals with smooth phases ⋮ Meromorphy of local zeta functions in smooth model cases ⋮ Nonpolar singularities of local zeta functions in some smooth case

Cites Work

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• Polyèdre de Newton et distribution \(f^ s_+\). I. (Newton polyhedra and distributions \(f^ s_+\). I.)
• Some local consequences of Hodge theory
• Newton polyhedron and \(f^ s_ +\) distribution. II
• Polyedres de Newton et nombres de Milnor
• Newton polyhedra and estimation of oscillating integrals
• Meromorphic property of the functions \(P^ \lambda\)
• Introduction to Toric Varieties. (AM-131)

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