Local Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields

Journal of Mathematical Sciences

León-Cardenal, E.¹  Zúñiga-Galindo, W. A.¹ 

关键词: $p$-adic oscillatory integrals;    Laurent polynomials;    Igusa zeta function;    Newton polytopes;    non-degeneracy conditions at infinity.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Inthisarticle,westudylocalzetafunctionsattachedtoLaurentpolynomialsover$p$-adicfields,whicharenon-degeneratewithrespecttotheirNewtonpolytopesatinfinity.Asanapplicationweobtainasymptoticexpansionsfor$p$-adicoscillatoryintegralsattachedtoLaurentpolynomials.Weshowtheexistenceoftwodifferentasymptoticexpansionsfor$p$-adicoscillatoryintegrals,onewhentheabsolutevalueoftheparameterapproachesinfinity,theotherwhentheabsolutevalueoftheparameterapproacheszero.ThesetwoasymptoticexpansionsarecontrolledbythepolesoftwistedlocalzetafunctionsofIgusatype.

【 授权许可】

Unknown