Lapkova, Kostadinka (2017) On the average number of divisors of reducible quadratic polynomials. Journal of Number Theory, 180. pp. 710-729. ISSN 0022-314X
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Official URL: https://doi.org/10.1016/j.jnt.2017.05.002
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. © 2017 Elsevier Inc.
| Item Type: | Article |
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| Additional Information: | N1 Funding details: FWF, Austrian Science Fund N1 Funding details: T846-N35, FWF, Austrian Science Fund N1 Funding details: K104183 N1 Funding text: This work was supported by the Austrian Science Fund (FWF) [T846-N35]; and partially by the National Research, Development and Innovation Office (NKFIH) [K104183]. |
| Uncontrolled Keywords: | Quadratic polynomial; number of divisors; Dirichlet series |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 21 Dec 2017 15:11 |
| Last Modified: | 21 Dec 2017 15:11 |
| URI: | http://real.mtak.hu/id/eprint/71570 |
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