no. 2
On the mean square of the divisor function in short intervals
Ivić, Aleksandar1
1 Katedra Matematike RGF-a Universitet u Beogradu, Đušina 7 11000 Beograd, Serbia
Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 2, pp. 251-261.

On donne des estimations pour la moyenne quadratique de

∫ X 2 X 𝔻 k ( x + h ) - 𝔻 k ( x ) 2 d x ,

où h=h(X)≫1,h=o(x) quand X→∞ et h se trouve dans un intervalle convenable. Pour k≥2 un entier fixé, 𝔻 k (x) et le terme d’erreur pour la fonction sommatoire de la fonction des diviseurs d k (n), generée par ζ k (s).

We provide upper bounds for the mean square integral

∫ X 2 X 𝔻 k ( x + h ) - 𝔻 k ( x ) 2 d x ,

where h=h(X)≫1,h=o(x) as X→∞ and h lies in a suitable range. For k≥2 a fixed integer, 𝔻 k (x) is the error term in the asymptotic formula for the summatory function of the divisor function d k (n), generated by ζ k (s).

DOI : 10.5802/jtnb.669
Ivić, Aleksandar 1

1 Katedra Matematike RGF-a Universitet u Beogradu, Đušina 7 11000 Beograd, Serbia 
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Ivić, Aleksandar. On the mean square of the divisor function in short intervals. Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 2, pp. 251-261. doi : 10.5802/jtnb.669. http://www.numdam.org/articles/10.5802/jtnb.669/

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