Riesz Criterion
It can be shown that
for any exponent e larger than 1/2, where this is big O notation; taking values both positive and negative. Riesz showed that the Riemann hypothesis is equivalent to the claim that the above is true for any e larger than 1/4. In the same paper, he added a slightly pessimistic note too: «Je ne sais pas encore decider si cette condition facilitera la vérification de l'hypothèse».
Read more about this topic: Riesz Function
Famous quotes containing the word criterion:
“... the condition of women affords, in all countries, the best criterion by which to judge the character of men.”
—Frances Wright (1795–1852)