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 1/2 + it with t a real number variable and i 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.
Famous quotes containing the words grand and/or hypothesis:
“One would like to be grand and heroic, if one could; but if not, why try at all? One wants to be very something, very great, very heroic; or if not that, then at least very stylish and very fashionable. It is this everlasting mediocrity that bores me.”
—Harriet Beecher Stowe (1811–1896)
“On pragmatistic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, it is true.”
—William James (1842–1910)