The set of zeros of the Riemann zeta function as the point spectrum of an operator

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-06-27 DOI:10.1090/spmj/1720

V. Kapustin

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引用次数: 0

Abstract

A possible way of proving the Riemann hypothesis consists of constructing a selfadjoint operartor whose spectrum coincides with the set { z : | Im ⁡ z | > 1 2 , ζ ( 1 2 − i z ) = 0 } \{z\,: \, |\operatorname {Im}z|>\frac 12, \ \zeta \big (\frac {1}{2}-iz\big )=0\} . In the paper we construct a rank-one perturbation of a selfadjoint operator related to a certain canonical system for which a similar property is fulfilled.

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作为算子的点谱的黎曼函数的零的集合

证明黎曼假说的一种可能的方法是构造一个自伴操纵子，其谱与集合{z:|Im一致⁡ z|>12，ζ（12−i z）=0｝\｛z\，：\，|\运算符名称{Im}z|>\frac 12，\\zeta\big（\frac｛1｝{2}-iz\big）=0\｝。在本文中，我们构造了一个自伴随算子的秩一微扰，它与一个具有相似性质的正则系统有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.