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:
“It enhances our sense of the grand security and serenity of nature to observe the still undisturbed economy and content of the fishes of this century, their happiness a regular fruit of the summer.”
—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)