On a Conjecture of Igusa in Two Dimensions

James Wright

Type: Article

Publication Date: 2020-01-01

Citations: 4

DOI: https://doi.org/10.1353/ajm.2020.0026

Abstract

We extend work of Denef and Sperber and also Cluckers regarding a conjecture of Igusa in the two dimensional setting by no longer requiring the polynomial to be nondegenerate with respect to its Newton diagram. More precisely we establish sharp, uniform bounds for complete exponential sums and the number of polynomial congruences for general quasi-homogeneous polynomials in two variables.

Locations

American Journal of Mathematics - View
Edinburgh Research Explorer (University of Edinburgh) - View - PDF

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Works Cited by This (11)

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+ PDF Chat	Elementary and Analytic Theory of Algebraic Numbers	1991	Peter Shiu Władysław Narkiewicz
+ PDF Chat	Exponential sums: Questions by Denef, Sperber, and Igusa	2009	Raf Cluckers
+	Oscillatory integrals with polynomial phases	1992	D. H. Phong E. M. Stein
+	On adapted coordinate systems	2011	Isroil A. Ikromov Detlef Müller
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+	On the growth and stability of real-analytic functions	1999	D. H. Phong E. M. Stein Jacob Sturm
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+ PDF Chat	Igusa and Denef-Sperber conjectures on nondegenerate p-adic exponential sums	2007	Raf Cluckers
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+	Algebraic Number Theory	1994	Serge Lang