Formal Statement
A mathematically precise statement of universality for the Riemann zeta-function ζ(s) follows.
Let U be a compact subset of the strip
such that the complement of U is connected. Let f : U → C be a continuous function on U which is holomorphic on the interior of U and does not have any zeros in U. Then for any ε > 0 there exists a t ≥ 0 such that
Even more: the lower density of the set of values t which do the job is positive, as is expressed by the following inequality about a limit inferior.
where λ denotes the Lebesgue measure on the real numbers.
Read more about this topic: Zeta Function Universality
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