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Explicit upper bound for an average number of divisors of quadratic polynomials

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Abstract

Consider the divisor sum \({\sum_{n\leq N} \tau(n^2+2bn+c)}\) for integers b and c which satisfy certain extra conditions. For this average sum, we obtain an explicit upper bound, which is close to the optimal. As an application we improve the maximal possible number of \({D(-1)}\)-quadruples.

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Correspondence to Kostadinka Lapkova.

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This work is partially supported by Hungarian Scientific Research Fund (OTKA) Grant No. K104183.

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Lapkova, K. Explicit upper bound for an average number of divisors of quadratic polynomials. Arch. Math. 106, 247–256 (2016). https://doi.org/10.1007/s00013-015-0862-2

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