trailAll non-trivial zeros of the Riemann zeta function have real part equal to 1/2.
All non-trivial zeros of every Dirichlet L-function have real part equal to 1/2.
Numerical verification and proven density results· for
The Riemann hypothesis has been verified for the first ten trillion non-trivial zeros of the zeta function.
All non-trivial zeros of the Riemann zeta function up to height 3×10^12 lie on the critical line.
Gourdon's 2004 computation found all of the first 10^13 non-trivial zeros of the Riemann zeta function on the critical line.
At least 40 percent of the non-trivial zeros of the Riemann zeta function lie on the critical line.
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Analogy with the proven finite-field case· for
The analogue of the Riemann hypothesis for zeta functions of varieties over finite fields is a proven theorem.
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Spectral and random-matrix heuristics· for
The spacing statistics of the zeros of the Riemann zeta function match those of eigenvalues of random Hermitian matrices.
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Claimed proofs· for
Michael Atiyah's 2018 claimed proof establishes the Riemann hypothesis.
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Skeptical considerations· against
The Davenport-Heilbronn function satisfies a Riemann-type functional equation yet has zeros off the critical line.
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All non-trivial zeros of the Riemann zeta function have real part equal to 1/2.
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