Meromorphic continuations of local zeta functions and their applications to oscillating integrals

DOI10.2748/tmj/1372182720zbMath1345.14010arXiv0903.4265OpenAlexW2012610454MaRDI QIDQ372600

Toshihisa Okada, Kiyoshi Takeuchi

Publication date: 9 October 2013

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.4265

zbMATH Keywords

toric varietyoscillating integrallocal zeta function

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Singularities in algebraic geometry (14B05) Maximal functions, Littlewood-Paley theory (42B25) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (5)

Archimedean zeta functions and oscillatory integrals ⋮ Resolution of singularities for \(C^\infty\) functions and meromorphy of local zeta functions ⋮ 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi
• Milnor fibers over singular toric varieties and nearby cycle sheaves
• Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves
• Polyèdre de Newton et distribution \(f^ s_+\). I. (Newton polyhedra and distributions \(f^ s_+\). I.)
• A geometric degree formula for \(A\)-discriminants and Euler obstructions of toric varieties
• Monodromy at infinity of \(A\)-hypergeometric functions and toric compactifications
• Oscillatory integral operators with homogeneous polynomial phases in several variables
• Newton polyhedra and estimation of oscillating integrals
• The distribution \(|v|^\lambda\), oscillating integrals and principal value integrals
• Conditions against rapid decrease of oscillatory integrals and their applications to inverse scattering problems
• Développement asymptotique des fonctions obtenues par intégration sur les fibres
• Oscillatory integral operators with low-order degeneracies.
• Oscillating integrals and Newton polyhedra
• An introduction to $p$-adic and motivic zeta functions and the monodromy conjecture
• Introduction to Toric Varieties. (AM-131)

This page was built for publication: Meromorphic continuations of local zeta functions and their applications to oscillating integrals