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arXiv · 0807.0090

A proof of the Riemann hypothesis

Xian-Jin Li
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Abstract

In this paper we study traces of an integral operator on two orthogonal subspaces of a $L^2$ space. One of the two traces is shown to be zero. Also, we prove that the trace of the operator on the second subspace is nonnegative. Hence, the operator has a nonnegative trace on the $L^2$ space. This implies the positivity of Li's criterion. By Li's criterion, all nontrivial zeros of the Riemann zeta-function lie on the critical line.

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Xian-Jin Li. 2008-07-01. A proof of the Riemann hypothesis. https://arxiv.org/abs/0807.0090

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