论文标题
涉及Dedekind Zeta函数的非平凡零的模块化关系，以及广义的Riemann假设
A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis
论文作者
论文摘要
我们给出了Ramanujan，Hardy和Littlewood的结果的数字类似物，从而获得了涉及Dedekind Zeta函数的非平凡零的模块化关系。我们还为$ζ_K（S）$的广义Riemann假设提供了Riesz型标准。当$ k $是二次扩展时，将获得新的优雅转换，其中之一涉及第二种修改后的贝塞尔功能。
We give a number field analogue of a result of Ramanujan, Hardy and Littlewood, thereby obtaining a modular relation involving the non-trivial zeros of the Dedekind zeta function. We also provide a Riesz-type criterion for the Generalized Riemann Hypothesis for $ζ_K(s)$. New elegant transformations are obtained when $K$ is a quadratic extension, one of which involves the modified Bessel function of the second kind.
