Gronwall’s theorem

The function

G(n):=σ(n)nln(lnn)  (n= 2, 3, 4,),

in which σ(n) means the sum of the positive divisors of n, satisfies the equation

lim supnG(n)=eγ

where γ is the Euler–Mascheroni constant.


  • 1 T. H. Gronwall:  Some asymptotic expressions in the theory of numbers.  - Trans. Amer. Math. Soc. 14 (1913) 113–122.
Title Gronwall’s theorem
Canonical name GronwallsTheorem
Date of creation 2013-03-22 19:33:44
Last modified on 2013-03-22 19:33:44
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Theorem
Classification msc 40A99
Classification msc 11A25
Classification msc 26A12
Related topic EulerMascheroniConstant
Related topic RobinsTheorem