Primes Represented by Binary Cubic Forms | Zendy

HeathBrown D. R. | Zendy; Moroz B. Z. | Zendy

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Primes Represented by Binary Cubic Forms

Author(s) -

HeathBrown D. R.,

Moroz B. Z.

Publication year - 2002

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/84.2.257

Subject(s) - mathematics , prime (order theory) , cubic form , binary number , combinatorics , prime number , mathematics subject classification , polynomial , set (abstract data type) , discrete mathematics , arithmetic , mathematical analysis , computer science , programming language

Let f ( x , y ) be a binary cubic form with integral rational coefficients, and suppose that the polynomial f ( x , y ) is irreducible in Q [ x , y ] and no prime divides all the coefficients of f . We prove that the set f Z (2) contains infinitely many primes unless f ( a , b ) is even for each ( a , b ) in Z 2 , in which case the set 1 2 f ( Z 2 ) contains infinitely many primes. 2000 Mathematical Subject Classification : primary 11N32; secondary 11N36, 11R44.

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