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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
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 x2 + 2αy2 + 2βz2 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) = x2 + 2αy2 + 2βz2 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 2t 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X2 + 2α是的2 + 2βz2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) = X2 + 2α是的2 + 2βz20 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 = 6, 7, 8由 eta 商组成。
更新日期:2020-09-24
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