Difference sets and the irreducibles in function fields | Zendy

Lê Thái Hoàng | Zendy; Spencer Craig V. | Zendy

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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 .

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