The regularity lemma is false over small fields
نویسندگان
چکیده
منابع مشابه
Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets
Let P : F × F → F be a polynomial of bounded degree over a finite field F of large characteristic. In this paper we establish the following dichotomy: either P is a moderate asymmetric expander in the sense that |P (A,B)| |F| whenever A,B ⊂ F are such that |A||B| ≥ C|F|2−1/8 for a sufficiently large C, or else P takes the form P (x, y) = Q(F (x) + G(y)) or P (x, y) = Q(F (x)G(y)) for some polyn...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2019
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2019.1684507