On the Physics of the Riemann Zeros

6th International Symposium on Quantum Theory and Symmetries

He, Yang-Hui^1,2,3,4 ; Jejjala, Vishnu^5 ; Minic, Djordje^6

Rudolf Peierls Centre for Theoretical Physics, Oxford University, 1 Keble Road, OX1 3NP, United Kingdom^1

Merton College, Oxford, OX1 4JD, United Kingdom^2

Department of Mathematics, City University, Northampton Square, London EC1V 0HB, United Kingdom^3

School of Physics, NanKai University, Tianjin, 300071, China^4

Centre for Research in String Theory, Department of Physics, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom^5

IPNAS, Department of Physics, Virginia Tech., Blacksburg, VA 24061, United States^6

关键词: Formal derivation;    Hilbert;    Non-trivial;    Physical interpretation;    Riemann hypothesis;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/462/1/012036/pdf
DOI  :  10.1088/1742-6596/462/1/012036

来源: IOP

【 摘 要 】

We discuss a formal derivation of an integral expression for the Li coefficients associated with the Riemann ξ-function which, in particular, indicates that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and discuss a physical interpretation of this result within the Hilbert-Po´lya approach. In this context we also outline a relation between string theory and the Riemann Hypothesis.