Abstract
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 language | English |
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Pages (from-to) | 710-729 |
Number of pages | 20 |
Journal | Journal of Number Theory |
Volume | 180 |
DOIs | |
Publication status | Published - 1 Nov 2017 |
Keywords
- Dirichlet series
- Number of divisors
- Quadratic polynomial
ASJC Scopus subject areas
- Algebra and Number Theory