WOLFRAM|DEMONSTRATIONS PROJECT

Logarithmic Integral on the Critical Line

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x
range of t
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In his 1859 paper "On the Number of Primes Less Than a Given Magnitude," Bernhard Riemann gave a formula involving his zeta function to determine the number of primes less than a specific number
x
. This Demonstration shows the behavior of the logarithmic integral
Li(
1/2+it
x
) that corresponds to the second or "periodic" terms as referred to by Riemann.