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

@article{JTNB_2009__21_2_251_0,
     author = {Ivi\'c, Aleksandar},
     title = {On the mean square of the divisor function in short intervals},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {2},
     year = {2009},
     pages = {251-261},
     doi = {10.5802/jtnb.669},
     mrnumber = {2541424},
     zbl = {pre05620649},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2009__21_2_251_0}
}
Ivić, Aleksandar. 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. http://www.numdam.org/item/JTNB_2009__21_2_251_0/

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