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Almost primes represented by binary forms
Author(s) -
Marasingha Gihan
Publication year - 2010
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdq026
Subject(s) - mathematics , binary number , product (mathematics) , prime (order theory) , integer (computer science) , degree (music) , polynomial , combinatorics , discrete mathematics , pure mathematics , arithmetic , mathematical analysis , physics , computer science , geometry , acoustics , programming language
We demonstrate that, under suitable local conditions on a finite collection F 1 ,…, F g of binary irreducible forms with integer coefficients, the product F 1 ( x )·…· F g ( x ) will have at most r prime factors for infinitely many x . We give explicit upper bounds for r that depend only on g and on the total degree of the product polynomial.
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