On the bias of cubic polynomials

David Kazhdan*, Tamar Ziegler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let V be a vector space over a finite field k= Fq of dimension N. For a polynomial P: V→ k we define the biasb~ 1(P) to be (Formula presented.) Nwhere ψ: k→ C is a non-trivial additive character. A. Bhowmick and S. Lovett proved that for any d≥ 1 and cCloseSPigtSPi 0 there exists r= r(d, c) such that any polynomial P of degree d with b~ 1(P) ≥ c can be written as a sum P=∑i=1rQiRi where Qi, Ri: V→ k are non constant polynomials. We show the validity of a modified version of the converse statement for the case d= 3.

Original languageAmerican English
Pages (from-to)511-520
Number of pages10
JournalSelecta Mathematica, New Series
Volume24
Issue number1
DOIs
StatePublished - 1 Mar 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing AG.

Keywords

  • 11T55

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