On the average number of divisors of reducible quadratic polynomials

Kostadinka Lapkova

Research output: Contribution to journalArticlepeer-review


We give an asymptotic formula for the divisor sum ∑c<n≤Nτ((n−b)(n−c)) for integers b<c of the same parity. Interestingly, the coefficient of the main term does not depend on the discriminant as long as it is a full square. We also provide effective upper bounds of the average divisor sum for some of the reducible quadratic polynomials considered before, with the same main term as in the asymptotic formula.

Original languageEnglish
Pages (from-to)710-729
Number of pages20
JournalJournal of Number Theory
Publication statusPublished - 1 Nov 2017


  • Dirichlet series
  • Number of divisors
  • Quadratic polynomial

ASJC Scopus subject areas

  • Algebra and Number Theory


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