Riemann hypothesis

Etymology
Named after German mathematician (1826–1866), who first formulated and discussed the hypothesis.

Proper noun

 * 1)  The conjecture that the zeros of the Riemann zeta function exist only at the negative even integers and certain complex numbers whose real part is ½.
 * 2) * 1995, John Corning Carey, On Beurling's Approach to the Reimann Hypothesis,, page 43,
 * But in the absence of such assumptions, the task of finding functions $$h\in\mathcal{F}_2$$ for which $$\left\Vert 1+h\right\Vert_2$$ is small is equivalent to proving the Riemann hypothesis, as we will now demonstrate.
 * 1) * 2003,, , 2004, HarperCollins Publishers (Harper Perennial), page 10,
 * A solution of the Riemann Hypothesis will have huge implications for many other mathematical problems.
 * 1) * 2010,, The Riemann Hypothesis – a short history, Gerrit Dijk, Masato Wakayama (editors), Casimir Force, Casimir Operators and the Riemann Hypothesis, Walter de Gruyter, page 30,
 * The one problem proposed in Riemann's paper which remained unproved, the only one Riemann put forward explicitly as a conjecture, was the Riemann Hypothesis.
 * 1) * 2021, Naji Arwashan, The Riemann Hypothesis and the Distribution of Prime Numbers,, page x,
 * The Riemann Hypothesis is considered by many accounts the single most important and difficult question in math today.
 * The Riemann Hypothesis is considered by many accounts the single most important and difficult question in math today.

Usage notes

 * The zeros at the negative even integers are conventionally called trivial. Thus, the hypothesis is often formulated as:
 * The real part of every nontrivial zero of the Riemann zeta function is $$\textstyle\frac 1 2$$.

Translations

 * French: hypothèse de Riemann
 * German: Riemannsche Vermutung, Riemann-Vermutung, Riemannsche Hypothese, Riemann-Hypothese
 * Italian: ipotesi di Riemann, congettura di Riemann