  A common problem in analytic number theory is to bound the sum of an
arithmetic function over a set of integers. Nair and Tenenbaum found a very
general bound that applies to short sums of a multivariable arithmetic function
over polynomial values, under certain standard conditions on the growth of that
function. Their bound features an implicit dependency on the discriminant of
the relevant polynomial. In our paper we obtain an analogous bound with an
explicit dependency on the discriminant, which is optimal in the discriminant
aspect.
