The parity problem for irreducible cubic forms

2005/01/12 by H. A. Helfgott, Helfgott, H. A.
Mathematics · #11N32 #11N35 #11N36 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N32 #msc:11N35 #msc:11N36

paper · pdf · doi:10.48550/arxiv.math/0501177

11 pages

arxiv created 2005/01/12 · arxiv updated 2009/12/01

Abstract

Let f∈ ℤ[x,y] be an irreducible homogeneous polynomial of degree 3. We show that f(x,y) has an even number of prime factors as often as an odd number of prime factors.

Related

• The parity problem for reducible cubic forms
• An effective analytic formula for the number of distinct irreducible factors of a polynomial
• Cubic polynomials represented by norm forms
• On forms in prime variables
• Another irreducibility criterion