Fourier analysis and expanding phenomena in finite fields

Details Fourier analysis and expanding phenomena in finite fields Fourier analysis and expanding phenomena in finite fields

2009-09-30

arxiv.org/abs/0909.5471v1

Mathematics

Number Theory

Scientific paper

In this paper the authors study set expansion in finite fields. Fourier analytic proofs are given for several results recently obtained by Solymosi, Vinh and Vu using spectral graph theory. In addition, several generalizations of these results are given. In the case that $A$ is a subset of a prime field $\mathbb F_p$ of size less than $p^{1/2}$ it is shown that $|\{a^2+b:a,b \in A\}|\geq C |A|^{147/146}$, where $|\cdot|$ denotes the cardinality of the set and $C$ is an absolute constant.

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