论文标题
与Zeta和$ l $ unctions的零插值
Fourier interpolation with zeros of zeta and $L$-functions
论文作者
论文摘要
我们构建了一个大型的傅立叶插值基础，以在对称真实线的对称性中进行函数分析。有趣的示例涉及Riemann Zeta功能和其他$ L $ functions的非平凡零。我们根据具有可变系数的一般dirichlet系列的某些内核来建立傅立叶插值基库的二元性原理。这样的内核允许meromorthic延续，两极的序列是dirichlet系列频率序列的序列，并且它们满足功能方程。我们的混凝土基础的构建依赖于通过功能方程的Dirichlet系列的Knopp的丰度原理的加强以及对相关的Dirichlet系列内核的仔细分析，其系数是由Theta组的某些模块化积分引起的。
We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other $L$-functions. We establish a duality principle for Fourier interpolation bases in terms of certain kernels of general Dirichlet series with variable coefficients. Such kernels admit meromorphic continuation, with poles at a sequence dual to the sequence of frequencies of the Dirichlet series, and they satisfy a functional equation. Our construction of concrete bases relies on a strengthening of Knopp's abundance principle for Dirichlet series with functional equations and a careful analysis of the associated Dirichlet series kernel, with coefficients arising from certain modular integrals for the theta group.
