论文标题
Theta系列和算术应用规范的统一界限
Uniform bounds for norms of theta series and arithmetic applications
论文作者
论文摘要
我们证明了theta系列的cuspidal部分的彼得森规范的统一界限。这为通过二次形式提供了改进的渐近公式，用于表示表示的数量。 As an application, we show that every integer $n \neq 0,4,7 \,(\operatorname{mod}8)$ is represented as $n= x_1^2 + x_2^2 + x_3^3$ for integers $x_1,x_2,x_3$ such that the product $x_1x_2x_3$ has at most 72 prime divisors.
We prove uniform bounds for the Petersson norm of the cuspidal part of the theta series. This gives an improved asymptotic formula for the number of representations by a quadratic form. As an application, we show that every integer $n \neq 0,4,7 \,(\operatorname{mod}8)$ is represented as $n= x_1^2 + x_2^2 + x_3^3$ for integers $x_1,x_2,x_3$ such that the product $x_1x_2x_3$ has at most 72 prime divisors.
