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  • Cited by 3
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kozyrev, S. V. 2011. Methods and applications of ultrametric and p-adic analysis: From wavelet theory to biophysics. Proceedings of the Steklov Institute of Mathematics, Vol. 274, Issue. S1, p. 1.


    Zuniga-Galindo, W. A. 2009. Local Zeta Functions Supported on Analytic Submanifolds and Newton Polyhedra. International Mathematics Research Notices,


    Zuniga-Galindo, W. A. 2005. Local zeta function for nondegenerate homogeneous mappings. Pacific Journal of Mathematics, Vol. 218, Issue. 1, p. 187.


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  • Bulletin of the London Mathematical Society, Volume 36, Issue 3
  • May 2004, pp. 310-320

ON THE POLES OF IGUSA'S LOCAL ZETA FUNCTION FOR ALGEBRAIC SETS

  • W. A. ZUNIGA-GALINDO (a1)
  • DOI: http://dx.doi.org/10.1112/S0024609303002947
  • Published online: 01 April 2004
Abstract

Let $K$ be a $p$-adic field, let $Z_{\Phi }(s,f)$, $s\,{\in}\,\mathbb{C}$, with Re$(s)\,{>}\,0$, be the Igusa local zeta function associated to $f(x)\,{=}\,(f_{1}(x),\ldots,f_{l}(x))\,{\in}\,[ K( x_{1},\ldots,x_{n})]^{l}$, and let $\Phi $ be a Schwartz–Bruhat function. The aim of this paper is to describe explicitly the poles of the meromorphic continuation of $Z_{\Phi }(s,f)$. Using resolution of singularities it is possible to express $Z_{\Phi }(s,f)$ as a finite sum of $p$-adic monomial integrals. These monomial integrals are computed explicitly by using techniques of toroidal geometry. In this way, an explicit list of the candidates for poles of $Z_{\Phi }(s,f)$ is obtained.

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Bulletin of the London Mathematical Society
  • ISSN: 0024-6093
  • EISSN: 1469-2120
  • URL: /core/journals/bulletin-of-the-london-mathematical-society
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