On the Extended, Generalized, and Grand Riemann Hypothesis for L-Functions

To study the non-trivial zero distribution of different kinds of $L$-functions, this paper generalizes the key lemma—Lemma 8 in reference [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.