A proof of the Riemann hypothesis

2008/07/01 by Xian-Jin Li, Li, Xian-Jin · 1 voice
#math.GM

paper · pdf · doi:10.48550/arxiv.0807.0090

Abstract

In this paper we study traces of an integral operator on two orthogonal subspaces of a L² 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 L² 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.

Discussions

• A proof of the Riemann hypothesis [hn, 15 points, 7 comments]

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