Explicit upper bound for the average number of divisors of irreducible quadratic polynomials.

Consider the divisor sum ∑n≤Nτ(n2+2bn+c) for integers b and c. We extract an asymptotic formula for the average divisor sum in a convenient form, and provide an explicit upper bound for this sum with the correct main term. As an application we give an improvement of the maximal possible number of D(-1) -quadruples.