Abstract: dvi (3K), pdf (70K), ps (26K).
Paper: dvi (20K), pdf (174K), ps (73K).
Phin(x) = Cn2 + nxDn2
of Aurifeuille, Le Lasseur and Lucas. Here Cn(x) and Dn(x) are monic polynomials with integer coefficients. These coefficients can be computed by simple algorithms which require O(n2) arithmetic operations over the integers. Also, there are explicit formulas and generating functions for Cn(x) and Dn(x). This paper is a preliminary report which states the results for the case n = 1 mod 4, and gives some numerical examples. The proofs, generalisations to other square-free n, and similar results for the identities of Gauss and Dirichlet, will appear in .
Go to next publication
Return to Richard Brent's index page