Formulae, originally conjectured by Liouville, are proved for the number of representations of a positive integer n by each of the eight sextenary quadratic forms x1 2 +x2 2+x 3 2 +x4 2+x5 2+4x6 2, x1 2 +x 2 2+x3 2+x4 2+4x5 2+4x6 2, x 1 2 +x2 2+x3 2 +4x4 2+4x5 2+4x6 2, x1 2+x2 2+4x 3 2 +4x4 2+4x5 2+4x6 2, x1 2 +4x 2 2+4x3 2+4x4 2+4x5 2+4x6 2, x 1 2 +x2 2+x3 2 +2x4 2+2x5 2+4x6 2, x1 2+x2 2+2x 3 2 +2x4 2+4x5 2+4x6 2, x1 2 +2x 2 2+2x3 2+4x4 2+4x5 2+4x6 2.

Additional Metadata
Keywords Liouville's formulae, Representations, Sextenary quadratic forms, Theta functions
Persistent URL dx.doi.org/10.1142/S1793042110002880
Journal International Journal of Number Theory
Citation
Alaca, A, Alaca, S, & Williams, K.S. (2010). Sextenary quadratic forms and an identity of Klein and Fricke. International Journal of Number Theory, 6(1), 169–183. doi:10.1142/S1793042110002880