Integrability at infinity of negative powers of polynomials in the plane and its application to convergence of Dirichlet series

DOI10.4064/sm210211-19-11zbMath1494.42015OpenAlexW4285281397WikidataQ114021979 ScholiaQ114021979MaRDI QIDQ5094155

Ha Huy Vui, Thi Thao Nguyen

Publication date: 2 August 2022

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/sm210211-19-11

zbMATH Keywords

Newton polygonDirichlet seriesweakly degenerate conditionMikhailov-Gindikin condition

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Dirichlet series, exponential series and other series in one complex variable (30B50) Inequalities involving derivatives and differential and integral operators (26D10) Real algebraic and real-analytic geometry (14P99)

Cites Work

• Unnamed Item
• On the integral criteria for a convergence of multidimensional Dirichlet series
• Milnor fibration at infinity
• Newton polygon and distribution of integer points in sublevel sets
• Convergence of two-dimensional weighted integrals
• Newton polyhedra and weighted oscillatory integrals with smooth phases
• A multi-dimensional resolution of singularities with applications to analysis
• On the volume and the number of lattice points of some semialgebraic sets
• On the growth and stability of real-analytic functions
• Nonpolar singularities of local zeta functions in some smooth case
• Newton polygons and local integrability of negative powers of smooth functions in the plane

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