2010-02-01
Sextenary quadratic forms and an identity of Klein and Fricke
Publication
Publication
International Journal of Number Theory
,
Volume 6
-
Issue 1
p. 169-
183
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
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