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

Kostadinka Lapkova

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

Number Theory 2015-10-21 v2

Authors: Kostadinka Lapkova

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.

Keywords

divisor sum quadratic polynomials upper bound average number of divisors D(-1)-quadruples

Cite

@article{arxiv.1509.08243,
  title  = {Explicit upper bound for an average number of divisors of quadratic polynomials},
  author = {Kostadinka Lapkova},
  journal= {arXiv preprint arXiv:1509.08243},
  year   = {2015}
}

Comments

Error in Lemma 2 corrected, 9 pages

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