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The number of representations of integers by generalized Bell ternary quadratic forms
International Journal of Number Theory ( IF 0.7 ) Pub Date : 2020-09-24 , DOI: 10.1142/s1793042121500135 Kyoungmin Kim 1 , Yeong-Wook Kwon 1
International Journal of Number Theory ( IF 0.7 ) Pub Date : 2020-09-24 , DOI: 10.1142/s1793042121500135 Kyoungmin Kim 1 , Yeong-Wook Kwon 1
Affiliation
For a positive definite ternary integral quadratic form f , let r ( n , f ) be the number of representations of an integer n by f . A ternary quadratic form f is said to be a generalized Bell ternary quadratic form if f is isometric to x 2 + 2 α y 2 + 2 β z 2 for some nonnegative integers α , β . In this paper, we give a closed formula for r ( n , f ) for a generalized Bell ternary quadratic form f ( x , y , z ) = x 2 + 2 α y 2 + 2 β z 2 with 0 ≤ α ≤ β ≤ 6 and class number greater than 1 by using the Minkowski–Siegel formula and bases for spaces of cusp forms of weight 3 2 and level 2 t with t = 6 , 7 , 8 consisting of eta-quotients.
中文翻译:
用广义贝尔三元二次形式表示的整数的数量
对于正定三元积分二次形式F , 让r ( n , F ) 是整数的表示数n 经过F . 三元二次型F 被称为广义贝尔三元二次形式,如果F 等距到X 2 + 2 α 是的 2 + 2 β z 2 对于一些非负整数α , β . 在本文中,我们给出了一个封闭公式r ( n , F ) 对于广义贝尔三元二次形式F ( X , 是的 , z ) = X 2 + 2 α 是的 2 + 2 β z 2 和0 ≤ α ≤ β ≤ 6 和类号大于1 通过使用 Minkowski-Siegel 公式和权重的尖角空间的基数3 2 和水平2 吨 和吨 = 6 , 7 , 8 由 eta 商组成。
更新日期:2020-09-24
中文翻译:
用广义贝尔三元二次形式表示的整数的数量
对于正定三元积分二次形式