Higher-order Fourier analysis of $mathbb{F} p^n$ and the complexity of systems of linear forms - Mathematics > Number TheoryReportar como inadecuado




Higher-order Fourier analysis of $mathbb{F} p^n$ and the complexity of systems of linear forms - Mathematics > Number Theory - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Consider a subset $A$ of $\mathbb{F} p^n$ and a decomposition of itsindicator function as the sum of two bounded functions $1 A=f 1+f 2$. For everyfamily of linear forms, we find the smallest degree of uniformity $k$ such thatassuming that $\|f 2\| {U^k}$ is sufficiently small, it is possible to discard$f 2$ and replace $1 A$ with $f 1$ in the average over this family of linearforms, affecting it only negligibly. Previously, Gowers and Wolf solved thisproblem for the case where $f 1$ is a constant function. Furthermore, our mainresult solves Problem 7.6 in W. T. Gowers and J. Wolf. Linear forms andhigher-degree uniformity for functions on $\mathbb{F} p^n$. Geom. Funct. Anal.,211:36-69, 2011 regarding the analytic averages that involve more than onesubset of $\mathbb{F} p^n$. regarding the analytic averages that involve morethan one subset of $\mathbb{F} p^n$.



Autor: Hamed Hatami, Shachar Lovett

Fuente: https://arxiv.org/







Documentos relacionados