论文标题
傅立叶优化和二次形式
Fourier optimization and quadratic forms
论文作者
论文摘要
我们使用傅立叶分析方法证明了以积极的确定二次形式表示的整数结果。特别是，对于整数$ \ ell \ geq 1 $，我们以$ \ ell $的倍数为倍数的整数的部分总和来改进错误项。这使我们能够以短时间的间隔获得无条件的Brun-titchmarsh型，并且有条件的cramér-type会导致以给定的正定二次形式表示的素数之间的最大差距。
We prove several results about integers represented by positive definite quadratic forms, using a Fourier analysis approach. In particular, for an integer $\ell\geq 1$, we improve the error term in the partial sums of the number of representations of integers that are a multiple of $\ell$. This allows us to obtain unconditional Brun-Titchmarsh-type results in short intervals, and a conditional Cramér-type result on the maximum gap between primes represented by a given positive definite quadratic form.
