A Unified Proof of the Extended, Generalized, and Grand Riemann Hypothesis

Source abstract

To study the non-trivial zero distribution of different kinds of L-functions, this paper generalizes the key lemma—Lemma 8 in Ref.[1] to Theorems 1-4. Based on Theorem 4, the Extended Riemann Hypothesis (for Dedekind zeta function), the Generalized Riemann Hypothesis (for Dirichlet L-function), and the Grand Riemann Hypothesis (for modular form L-function, automorphic L-function, and etc.) are proved under a unified framework based on the divisibility in the symmetrical functional equation of completed L-functions represented as Hadamard products.