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Explicit upper bound for the average number of divisors of irreducible quadratic polynomials (1704.02498v3)

Published 8 Apr 2017 in math.NT

Abstract: Consider the divisor sum $\sum_{n\leq N}\tau(n2+2bn+c)$ 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.

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