Representations of binary forms by certain quinary positive integral quadratic forms
Let \(f:= 2(\sum_{i=1}^4 x_i^2+ 2x_5^2- x_1x_2- x_2x_3- x_3x_4)\) and \(g:= 2(\sum_{i=1}^4 x_i^2+ 3x_5^2- x_1x_2- x_1x_3- x_1x_4- x_1x_5+ x_2x_5+ x_3x_5)\). It is proved that \(f\) represents all but one and \(g\) represents all but three binary positive even \(\mathbb{Z}\)-lattices. (This answers a question by Kitaoka.) Furthermore representations of binary quadratic forms by quinary quadratic forms in certain positive even 2-universal genera of class number 2 are investigated.
representations of binary quadratic forms
scientific article; zbMATH DE number 1749024
scientific article