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 of my playmates, who was apprenticed to a printer, and was somewhat of a wag, asked his master one afternoon if he might go a-fishing, and his master consented. He was gone three months. When he came back, he said that he had been to the Grand Banks, and went to setting type again as if only an afternoon had intervened.”
—Henry David Thoreau (1817–1862)
“It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.”
—Ludwig Wittgenstein (1889–1951)