Volume 36, Issue 3
Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function

Anal. Theory Appl., 36 (2020), pp. 283-294.

Published online: 2020-09

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• Abstract

The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same.

• Keywords

Hilbert-Pόlya space, zeros of zeta function, differential operator, eigenvalue.

11M06, 11Q20, 46A15

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@Article{ATA-36-283, author = {Liming Ge , and Xian-Jin Li , and Dongsheng Wu , and Boqing Xue , }, title = {Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {3}, pages = {283--294}, abstract = {

The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-SU1}, url = {http://global-sci.org/intro/article_detail/ata/18287.html} }
TY - JOUR T1 - Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function AU - Liming Ge , AU - Xian-Jin Li , AU - Dongsheng Wu , AU - Boqing Xue , JO - Analysis in Theory and Applications VL - 3 SP - 283 EP - 294 PY - 2020 DA - 2020/09 SN - 36 DO - http://doi.org/10.4208/ata.OA-SU1 UR - https://global-sci.org/intro/article_detail/ata/18287.html KW - Hilbert-Pόlya space, zeros of zeta function, differential operator, eigenvalue. AB -

The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same.

Liming Ge, Xian-Jin Li, Dongsheng Wu & Boqing Xue. (2020). Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function. Analysis in Theory and Applications. 36 (3). 283-294. doi:10.4208/ata.OA-SU1
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