A stratification result for an exponential sum modulo p²

2020/02/26 by Lapkova, Kostadinka, Xiao, Stanley Yao
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2002.11657

Abstract

In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials F(x₁, ⋯, x_n) ∈ ℤ[x₁, ⋯, x_n] in the quotient ring ℤ/p²ℤ. We provide an estimate of this exponential sum and a corresponding stratification of the space \mathbbA_\mathbbF_pⁿ, which in particular illustrates a general stratification theorem of Fouvry and Katz.

Related

• Stratification theorems for exponential sums in families
• On a uniform bound for exponential sums modulo p^m for Deligne polynomials
• Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
• Exponential sums on Aⁿ, III
• On exponential sums