Igusa and Denef-Sperber Conjectures on nondegenerate p-adic exponential sums

2006/06/12 by Raf Cluckers, Cluckers, R. · 1 citation
Mathematics · #11L07 #11S40 (Primary) 11L05 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0606269

openalex publication_date 2006/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the intersection of Igusa's Conjecture of [Igusa, J., "Lectures on forms of higher degree", Lect. math. phys., Springer-Verlag, 59 (1978)] and the Denef - Sperber Conjecture of [Denef, J. and Sperber, S., "Exponential sums mod pⁿ and Newton polyhedra", Bull. Belg. Math. Soc., suppl. (2001) 55-63] on nondegenerate exponential sums modulo p^m.

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• Exponential sums: questions by Denef, Sperber, and Igusa

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