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.
Bibliographical noteFunding Information:
The Tamar Ziegler is supported by ERC Grant ErgComNum 682150.
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