where
is the Euler-Mascheroni constant. Dirichlet
originally gave (Hardy and Wright 1979, p. 264; Hardy
1999, pp. 67-68), and Hardy and Landau showed in 1916 that (Hardy 1999, p. 81). The following table
summarizes incremental progress on the upper limit (updating Hardy 1999, p. 81).
approx.
citation
1/2
0.50000
Dirichlet
1/3
0.33333
Voronoi
(1903), Sierpiński (1906), van der Corput (1923)
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