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

Nair-Tenenbaum bounds uniform with respect to the discriminant