National Mathematics Contest
Award Ceremony
In mathematics, the Riemann hypothesis (German: Riemannsche Vermutung, abbr. RH) is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and at complex numbers with real part 1/2. The hypothesis was proposed by the German mathematician Bernhard Riemann (1859), from whom it takes its name. The term is also used for several closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The figure shows the real part (red) and imaginary part (blue) of the Riemann zeta function ζ(s) (s = 1/2 + ix). The first nontrivial zeros appear at Im(s) = x = ±14.135, ±21.022 and ±25.011.
The trajectory of a point moving along the critical line (s = 1/2 + ix) when mapped by the zeta function, forms a curve that repeatedly passes through the origin.
When the real part of s is varied, the trajectory drawn by the zeta function changes. For Re(s) = 1/2, the trajectory again forms a curve that repeatedly passes through the origin.
Artist's commentary
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