On the mean square of the divisor function in short intervals
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 2, pp. 251-261.

We provide upper bounds for the mean square integral

X2X𝔻k(x+h)-𝔻k(x)2dx,

where h=h(X)1,h=o(x) as X and h lies in a suitable range. For k2 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).

On donne des estimations pour la moyenne quadratique de

X2X𝔻k(x+h)-𝔻k(x)2dx,

h=h(X)1,h=o(x) quand X et h se trouve dans un intervalle convenable. Pour k2 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).

DOI: 10.5802/jtnb.669
Aleksandar Ivić 1

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

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