On spectral theory of the Riemann zeta function

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（11）
• 页码范围: 2317-2330
• 页数: 14页
• 语种: 英文

摘要

Every nontrivial zero of the Riemann zeta function is associated as eigenvalue with an eigenfunction of the fundamental differential operator on a Hilbert-Pólya space.It has geometric multiplicity one.A relation between nontrivial zeros of the zeta function and eigenvalues of the convolution operator is given.It is an analogue of the Selberg transform in Selberg's trace formula.Elements of the Hilbert-Pólya space are characterized by the Poisson summation formula.