Liouville's asserted formulae for the number of representations of a positive integer by each of the sextenary quadratic forms x2 + y2 + z2 + t2 + 2u2 + 2v2, x2 + y2 + 2z2 + 2t2 + 2u2 + 2v2and x2 + 2y2 + 2z2 + 2t2 + 2u2 + 4v2are proved.

Additional Metadata
Keywords Representations, Sextenary quadratic form s, Theta functions
Journal Far East Journal of Mathematical Sciences
Citation
Alaca, A, Alaca, S, & Williams, K.S. (2008). Liouville's sextenary quadratic forms x2 + y2 + z2 + t2 + 2u2 + 2v2, x2 + y2 + 2z2 + 2t2 + 2u2 + 2v2 and x2 + 2y2 + 2z2 + 2t2 + 2u2 + 4v2. Far East Journal of Mathematical Sciences, 30(3), 547–556.