A Proof Frame for Riemann Hypothesis

The Riemann hypothesis is a well-known mathematical problem that has been in suspense for 167 years. Its difficulty lies in the fact that the related Xi function (which shares same nontrivial zeros with the Zeta function) is involved in an infinite integral which includes infinite series with complex variable. To detour this is in vain, since all the messages are hid in it. To interpret them, there is a totally new idea, that is, to deduce an explicit symmetric formula for it. This is achieved by making prior estimations and generalizing the Gamma function. A total of three formulas are derived. Particularly, the third one in form of infinite series not only approaches the known zero-points with extremely high precision, but also meets the requirements of theoretical derivation. A possible proof frame for Riemann hypothesis is constructed by this. The missing parts are related to the complex calculations of combination numbers. Maybe the artificial-intelligence (AI) softwares are helpful. I look forward to the researchers working together to complete the proof. In addition, a possible distribution law of zero-points on the critical line was also found.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-28
DOI
https://doi.org/10.5281/zenodo.20423478
Primary Topic
Mathematical and Theoretical Analysis
Type
preprint
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preprint

A Proof Frame for Riemann Hypothesis

Jin-Liang Wang
Zenodo (CERN European Organization for Nuclear Research)
Mathematical and Theoretical Analysis
preprint

A Proof Frame for Riemann Hypothesis

Jin-Liang Wang
preprint en

Abstract

The Riemann hypothesis is a well-known mathematical problem that has been in suspense for 167 years. Its difficulty lies in the fact that the related Xi function (which shares same nontrivial zeros with the Zeta function) is involved in an infinite integral which includes infinite series with complex variable. To detour this is in vain, since all the messages are hid in it. To interpret them, there is a totally new idea, that is, to deduce an explicit symmetric formula for it. This is achieved by making prior estimations and generalizing the Gamma function. A total of three formulas are derived. Particularly, the third one in form of infinite series not only approaches the known zero-points with extremely high precision, but also meets the requirements of theoretical derivation. A possible proof frame for Riemann hypothesis is constructed by this. The missing parts are related to the complex calculations of combination numbers. Maybe the artificial-intelligence (AI) softwares are helpful. I look forward to the researchers working together to complete the proof. In addition, a possible distribution law of zero-points on the critical line was also found.

Zenodo (CERN European Organization for Nuclear Research)
Qingdao University of Technology (CN)
Peace, Justice and strong institutions
Mathematical and Theoretical Analysis
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