Definition
The Riemann ξ function is given by
where ζ is the Riemann zeta function. Consider the sequence
Li's criterion is then the statement that
- the Riemann hypothesis is completely equivalent to the statement that for every positive integer n.
The numbers may also be expressed in terms of the non-trivial zeros of the Riemann zeta function:
![\lambda_n=\sum_{\rho} \left[1-
\left(1-\frac{1}{\rho}\right)^n\right]](http://upload.wikimedia.org/math/5/3/c/53c989545cbb61055031c11698511747.png)
where the sum extends over ρ, the non-trivial zeros of the zeta function. This conditionally convergent sum should be understood in the sense that is usually used in number theory, namely, that
Read more about this topic: Li's Criterion
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