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ON THE MEAN VALUES OF THE HOMOGENEOUS DEDEKIND SUMS AND COCHRANE SUMS IN SHORT INTERVALS

ON THE MEAN VALUES OF THE HOMOGENEOUS DEDEKIND SUMS AND COCHRANE SUMS IN SHORT INTERVALS

In this paper, we study the mean values of the homogeneous Dedekind sums and Cochrane sums in short intervals <TEX>$[1,\;\frac{p}{3}]\;and\;[1,\;\frac{p}{4}]$</TEX>, and give some asymptotic formulae by using the mean values of the Dirichlet L-functions.