• Corpus ID: 18035601

# A proof of the Riemann hypothesis

@article{Li2008APO,
title={A proof of the Riemann hypothesis},
author={Xian-jin Li},
journal={arXiv: Number Theory},
year={2008}
}
• Xian-jin Li
• Published 1 July 2008
• Mathematics, Philosophy
• arXiv: Number Theory
In this paper, we prove that all nontrivial zeros of the Riemann zeta function lie on the line Rs = 1/2.
3 Citations

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## References

SHOWING 1-10 OF 17 REFERENCES

### The Positivity of a Sequence of Numbers and the Riemann Hypothesis

Abstract In this note, we prove that the Riemann hypothesis for the Dedekind zeta function is equivalent to the nonnegativity of a sequence of real numbers.

### Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

Abstract. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric

### Hilbert Space: Compact Operators and the Trace Theorem

1. Preliminaries 2. Orthogonality 3. Isomorphisms and isometries 4. Bounded linear operators 5. Elementary spectral theory 6. Self-adjoint operators 7. Compact operators on Hilbert space 8. Square

### Remarks on Weil’s quadratic functional in the theory of prime numbers, I

— This Memoir studies Weil’s well-known Explicit Formula in the theory of prime numbers and its associated quadratic functional, which is positive semidefinite if and only if the Riemann Hypothesis

### Problems of the Millennium : the Riemann Hypothesis

with s = 12 + it , and shows that ξ(t) is an even entire function of t whose zeros have imaginary part between −i/2 and i/2. He further states, sketching the proof, that in the range between 0 and T

### A Treatise on the Theory of Bessel Functions

THE memoir in which Bessel, the astronomer, examined in detail the functions which now bear his name was published in 1824, and was the outcome of his earlier researches concerning the expression of

### SUR LES FORMULES EXPLICITES DE LA THÉORIE DES NOMBRES

"Explicit formulas" in number theory express the sum of values of a function at the zeros of an L-series of an algebraic number field as a sum of local terms corresponding to all norms of this field.

### An Introduction to Abstract Harmonic Analysis

An introduction to abstract harmonic analysis is one of the literary work in this world in suitable to be reading material and it will show you the amazing benefits of reading a book.