论文标题
分解的效果
Etudes of the resolvent
论文作者
论文摘要
根据分解和希尔伯特身份的概念，本文从统一的角度来看，在差异操作员理论及其在自动形函数理论和数字理论中的某些应用中提出了许多经典结果。例如，对于Sturm-liouville操作员，Gelfand-Levitan痕量公式有一个推导，对于一维Schroedinger操作员，Faddeev的特征性决定性和Zakharov-faddeev Faddeev tendiatition的公式的推导。然后提出了关于在保形场理论中产生的特定功能差异算子的光谱理论的最新结果。调查的最后一部分专门针对Lobachevsky飞机上第一类的基本域的Laplace操作员。给出了一个代数方案，用于证明Laplace操作员和Eisenstein-Maass系列的分解的积分内核的分析延续。总而言之，人们讨论了Heegner Points Eisenstein-Maass系列的价值与虚构二次领域的Dedekind Zeta命令之间的关系，并且解释了为什么模块化组的伪cuSpforms为模块化组而言没有提供有关Riemann Zeta-Funcunter Zeros Zeros of Zeros for的情况。
Based on the notion of the resolvent and on the Hilbert identities, this paper presents a number of classical results in the theory of differential operators and some of their applications to the theory of automorphic functions and number theory from a unified point of view. For instance, for the Sturm-Liouville operator there is a derivation of the Gelfand-Levitan trace formula, and for the one-dimensional Schroedinger operator a derivation of Faddeev's formula for the characteristic determinant and the Zakharov-Faddeev trace identities. Recent results on the spectral theory of a certain functional-difference operator arising in conformal field theory are then presented. The last section of the survey is devoted to the Laplace operator on a fundamental domain of a Fuchsian group of the first kind on the Lobachevsky plane. An algebraic scheme is given for proving analytic continuation of the integral kernel of the resolvent of the Laplace operator and the Eisenstein-Maass series. In conclusion, there is a discussion of the relation between the values of the Eisenstein-Maass series at Heegner points and Dedekind zeta-functions of imaginary quadratic fields, and it is explained why pseudo-cuspforms for the case of the modular group do not provide any information about the zeros of the Riemann zeta-function.
