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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 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. == Notes == * It is widely believed that all global ''L''-functions are automorphic ''L''-functions. * 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Grand Riemann hypothesis」の詳細全文を読む スポンサード リンク
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