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On the mean square of the divisor function in short intervals

Aleksandar Ivić (2009)

Journal de Théorie des Nombres de Bordeaux

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 ) .

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