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The distribution of polynomials over finite fields, with applications to the Gowers norms

Abstract:

In this paper we investigate the uniform distribution properties of polynomials in many variables and bounded degree over a fixed finite field F of prime order. Our main result is that a polynomial P : F^n -> F is poorly-distributed only if P is determined by the values of a few polynomials of lower degree, in which case we say that P has small rank. We give several applications of this result, paying particular attention to consequences for the theory of the so-called Gowers norms. We e...

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Publication date:
2007-11-20
URN:
uuid:2a7dcea1-3072-46a2-a802-16eeeaa22247
Source identifiers:
398481
Local pid:
pubs:398481
Keywords:

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