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Journal of the London Mathematical Society 2006 73(2):415-435; doi:10.1112/S0024610706022629
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© The London Mathematical Society

The Parity Problem for Reducible Cubic Forms

H. A. Helfgott

Département de Mathématiques et Statistique, Université de Montréal CP 6128 succ Centre-Ville, Montréal, Québec, H3C 3J7, Canada helfgott{at}dms.umontreal.ca

Received 10 August 2004. Revision received 26 September 2005.

Let f isin Z[x,y] be a reducible 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.


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