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

TL;DR

This paper proves the combined conjecture of Igusa and Denef-Sperber regarding nondegenerate p-adic exponential sums, advancing understanding of their behavior modulo p^m.

Contribution

It establishes the intersection of two major conjectures on exponential sums, providing a unified proof for nondegenerate cases.

Findings

Proof of Igusa's conjecture for nondegenerate sums

Verification of Denef-Sperber conjecture in the same setting

Enhanced understanding of exponential sums modulo p^m

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 p^n and Newton polyhedra", Bull. Belg. Math. Soc., suppl. (2001) 55-63] on nondegenerate exponential sums modulo p^m.