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20112019

x_{1}^{2} + 2 x_{2}^{2} + x_{3}^{2} + x_{4}^{2} + x_{1} x_{3} + x_{1} x_{4} + x_{2} x_{4}

1 citations · 2 across the 2 of their papers we have counts for

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math.NT2019★ 1 cited

On some extension of Gauss' work and applications

Ho Yun Jung, Ja Kyung Koo, Dong Hwa Shin

Let $K$ be an imaginary quadratic field of discriminant $d_{K}$ , and let $n$ be a nontrivial integral ideal of $K$ in which $N$ is the smallest positive integer. Let $\mat…

math.NT2012

Some applications of modular units

Ick Sun Eum, Ja Kyung Koo, Dong Hwa Shin

We show that a weakly holomorphic modular function can be written as a sum of modular units of higher level. We further find a necessary and sufficient condition for a Siegel modul…

math.NT2011★ 1 cited

Representations by $x_{1}^{2} + 2 x_{2}^{2} + x_{3}^{2} + x_{4}^{2} + x_{1} x_{3} + x_{1} x_{4} + x_{2} x_{4}$

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 $Q = x_{1}^{2} + 2 x_{2}^{2} + x_{3}^{2} + x_{4}^{2} + x_{1} x_{3} + x_{1} x_{4} + x_{2} x_{4}$ . We first prove the identi…

On some extension of Gauss' work and applications

Some applications of modular units

Representations by x12​+2x22​+x32​+x42​+x1​x3​+x1​x4​+x2​x4​

Representations by $x_{1}^{2} + 2 x_{2}^{2} + x_{3}^{2} + x_{4}^{2} + x_{1} x_{3} + x_{1} x_{4} + x_{2} x_{4}$