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:
“That grand drama in a hundred acts, which is reserved for the next two centuries of Europe—the most terrible, most questionable and perhaps also the most hopeful of all dramas.”
—Friedrich Nietzsche (1844–1900)
“The great tragedy of science—the slaying of a beautiful hypothesis by an ugly fact.”
—Thomas Henry Huxley (1825–95)