By using Fourier analysis on number fields, we prove in this paper E.
Bombieri's refinement of A. Weil's positivity condition, which implies the
Riemann hypothesis for the Riemann zeta function in the spirit of A. Connes'
approach to the Riemann hypothesis.

http://arxiv.org/list/math/new

80] arXiv:0807.0090 (replaced) [ps, pdf, other]
Title: A proof of the Riemann hypothesis
Authors: Xian-Jin Li
Subjects: Number Theory (math.NT)
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The author admitted: "To avoid the complication of writings, I only considered the
rational number
field in this paper. But, I feel that techniques of this paper can be adopted to
any algebraic number field without much difficulty to give a proof of the Riemann
hypothesis for Dedeking (sic!) zeta functions."

Update: The paper has now been withdrawn by the author, “due to a mistake on pg. 29″.