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<h1 align=center> Equivalences involving primes
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The main point of [\begin{rawhtml}<a href="http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta">Riemann's original paper</a>\end{rawhtml}] of 1859 is that the two sequences, of prime numbers on the one hand, and of zeros of $\zeta$ on the other hand, are in duality. A precise mathematical formulation of this fact is given by the so-called explicit formulas of prime number theory (Riemann, von Mangoldt, Guinand, Weil). Therefore, any statement about one of these two sequences must have a translation in terms of the other. This is the case for the Riemann hypothesis.\begin{rawhtml}
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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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