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Difference sets and the irreducibles in function fields
Author(s) -
Lê Thái Hoàng,
Spencer Craig V.
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq106
Subject(s) - monic polynomial , mathematics , function field , polynomial , finite field , degree (music) , field (mathematics) , function (biology) , combinatorics , element (criminal law) , set (abstract data type) , discrete mathematics , pure mathematics , mathematical analysis , physics , evolutionary biology , political science , acoustics , law , computer science , biology , programming language
Let A be a subset of the polynomials of degree less than N over a finite field q . Let r be any nonzero element of q . We show that if the difference set A − A does not contain elements of the form P + r , where P is a monic, irreducible polynomial, then | A |⩽ C q N − c ( N /log N ) , where C and c are constants depending only on q .