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<h1 align=center> The Generalized Riemann Hypothesis
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The Generalized Riemann Hypothesis(GRH) is the assertion that the 
\begin{rawhtml}<a href="../16a">Riemann Hypothesis</a>\end{rawhtml} is true, and in addition the
\begin{rawhtml}<a href="../64a">nontrivial zeros</a>\end{rawhtml} of
all \begin{rawhtml}<a href="../9a">Dirichlet $L$-functions</a>\end{rawhtml}
lie on the \begin{rawhtml}<a href="../64a">critical line</a>\end{rawhtml} $\sigma=\frac12$.

Equivalently, GRH asserts that the nontrivial zeros of all
\begin{rawhtml}<a href="../11a">degree 1</a>\end{rawhtml} $L$-functions lie on the critical line.

The Modified Generalized Riemann Hypothesis(MGRH) is the assertion 
that the 
\begin{rawhtml}<a href="../16a">Riemann Hypothesis</a>\end{rawhtml} is true, and in addition the
\begin{rawhtml}<a href="../64a">nontrivial zeros</a>\end{rawhtml} of
all \begin{rawhtml}<a href="../9a">Dirichlet $L$-functions</a>\end{rawhtml}
lie either on the \begin{rawhtml}<a href="../64a">critical line</a>\end{rawhtml} $\sigma=\frac12$
or on the real axis.


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Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
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