Abstract

We give explicit bounds on sums of d(n)2d(n)^2 and d4(n)d_4(n), where d(n)d(n) is the number of divisors of nn and d4(n)d_4(n) is the number of ways of writing nn as a product of four numbers. In doing so we make a slight improvement on the upper bound for class numbers of quartic number fields.

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