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Algebras and Representation Theory

, Volume 21, Issue 5, pp 1017–1021 | Cite as

On Ranks of Polynomials

  • David Kazhdan
  • Tamar Ziegler
Article
  • 21 Downloads

Abstract

Let V be a vector space over a field k, P : Vk, 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 : Vk of degree d such that rank(P/t) ≤ r for all tV − 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 = .

Mathematics Subject Classification (2010)

11B30 14J99 

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Copyright information

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

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsGivaat Ram The Hebrew University of JerusalemJerusalemIsrael

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