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<h1 align=center> 100 percent hypothesis
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The 100\% Hypothesis for $L(s)$ asserts that 
$$
N_0(T) \sim N(T) .
$$
Here $N(T)$ is the \begin{rawhtml}<a href="../64a">zero counting function</a>\end{rawhtml}
for $L(s)$, and $N_0(T)$ counts only the zeros
on the \begin{rawhtml}<a href="../64a">critical line</a>\end{rawhtml}.  In other
words, 100 percent of the nontrivial zeros (in the sense
of density) are on the critical line.
An equivalent assertion is
$$
N(T)- N_0(T) = o(T\log T) ,
$$
which makes it clear that the 100\% Hypothesis still
allows quite a few zeros off the critical line.

The term ``100\% Hypothesis'' is not standard.

In contrast to most of the other conjectures in
this section, the 100\% Hypothesis is not motivated
by applications to the prime numbers.   
Indeed, at
present there are no known consequences of
this hypothesis.

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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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