Английская Википедия:Grand Riemann hypothesis

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In mathematics, the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and generalized Riemann hypothesis. It states that the nontrivial zeros of all automorphic L-functions lie on the critical line <math>\frac{1}{2} + it</math> with <math>t</math> a real number variable and <math>i</math> the imaginary unit.

The modified grand Riemann hypothesis is the assertion that the nontrivial zeros of all automorphic L-functions lie on the critical line or the real line.

Notes

• Robert Langlands, in his general functoriality conjectures, asserts that all global L-functions should be automorphic.
• The Siegel zero, conjectured not to exist, is a possible real zero of a Dirichlet L-series, rather near s = 1.
• L-functions of Maass cusp forms can have trivial zeros which are off the real line.

Further reading

• Шаблон:Citation