Representations by $x_1^2+2x_2^2+x_3^2+x_4^2+x_1{x}_3+x_1{x}_4+x_2{x}_4$

Ick Sun Eum, Dong Hwa Shin, Dong Sung Yoon

Let $r_Q(n)$ be the representation number of a nonnegative integer $n$ by the quaternary quadratic form $Q=x_1^2+2x_2^2+x_3^2+x_4^2+x_1{x}_3+x_1{x}_4+x_2{x}_4$. We first prove the identi…