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Counting integer points on quadrics with arithmetic weights
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2020-08-06 , DOI: 10.1090/tran/8154
V. Vinay Kumaraswamy

Let $F \in \mathbf{Z}[\boldsymbol{x}]$ be a diagonal, non-singular quadratic form in $4$ variables. Let $\lambda(n)$ be the normalised Fourier coefficients of a holomorphic Hecke form of full level. We give an upper bound for the problem of counting integer zeros of $F$ with $|\boldsymbol{x}| \leq X$, weighted by $\lambda(x_1)$.

中文翻译:

用算术权重计算二次曲面上的整数点

令 $F \in \mathbf{Z}[\boldsymbol{x}]$ 是 $4$ 变量中的对角线非奇异二次型。令 $\lambda(n)$ 是全级全纯 Hecke 形式的归一化傅立叶系数。我们给出了用 $|\boldsymbol{x}| 计算 $F$ 的整数零的问题的上限。\leq X$,由 $\lambda(x_1)$ 加权。
更新日期:2020-08-06
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