A stratification result for an exponential sum modulo p2

Kostadinka Lapkova; Stanley Yao Xiao

A stratification result for an exponential sum modulo p2

Kostadinka Lapkova, Stanley Yao Xiao

Institute of Analysis and Number Theory (5010)

Research output: Working paper › Preprint

Abstract

In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials $F(x_1, \cdots, x_n) \in \mathbb{Z}[x_1, \cdots, x_n]$ in the quotient ring $\mathbb{Z}/p^2\mathbb{Z}$. We provide an estimate of this exponential sum and a corresponding stratification of the space $\mathbb{A}_{\mathbb{F}_p}^n$, which in particular illustrates a general stratification theorem of Fouvry and Katz.

Original language	English
Number of pages	6
Publication status	Published - 26 Feb 2020

Publication series

Name	arXiv.org e-Print archive
Publisher	Cornell University Library

Keywords

math.NT

Fields of Expertise

Information, Communication & Computing

Access to Document

https://arxiv.org/abs/2002.11657Licence: Other

Cite this

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title = "A stratification result for an exponential sum modulo p2",

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N2 - In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials $F(x_1, \cdots, x_n) \in \mathbb{Z}[x_1, \cdots, x_n]$ in the quotient ring $\mathbb{Z}/p^2\mathbb{Z}$. We provide an estimate of this exponential sum and a corresponding stratification of the space $\mathbb{A}_{\mathbb{F}_p}^n$, which in particular illustrates a general stratification theorem of Fouvry and Katz.

AB - In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials $F(x_1, \cdots, x_n) \in \mathbb{Z}[x_1, \cdots, x_n]$ in the quotient ring $\mathbb{Z}/p^2\mathbb{Z}$. We provide an estimate of this exponential sum and a corresponding stratification of the space $\mathbb{A}_{\mathbb{F}_p}^n$, which in particular illustrates a general stratification theorem of Fouvry and Katz.

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M3 - Preprint

T3 - arXiv.org e-Print archive

BT - A stratification result for an exponential sum modulo p2

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