On Ranks of Polynomials

David Kazhdan*, Tamar Ziegler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Let V be a vector space over a field k, P : V → k, d ≥ 3. We show the existence of a function C(r, d) such that rank(P) ≤ C(r, d) for any field k, char(k) > d, a finite-dimensional k-vector space V and a polynomial P : V → k of degree d such that rank(∂P/∂t) ≤ r for all t ∈ V − 0. Our proof of this theorem is based on the application of results on Gowers norms for finite fields k. We don’t know a direct proof even in the case when k = ℂ.

Original languageAmerican English
Pages (from-to)1017-1021
Number of pages5
JournalAlgebras and Representation Theory
Issue number5
StatePublished - 1 Oct 2018

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© 2018, Springer Science+Business Media B.V., part of Springer Nature.


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