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<h1 align=center> Axiom 4: Euler Product
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$$
F(s)=\prod_p F_p(s),
$$
where the product is over the rational primes.
Here
$$
F_p(s)=\exp\left(\sum_{k=1}^\infty \frac{b_{p^k}}{p^{ks }} \right) 
$$
with $b_n\ll n^\theta$ for some $\theta<\frac12$.

Note that this implies $a_1=1$, so $F(s)=1$ is the only
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<p> <br>
Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
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