Note on the number of divisors of reducible quadratic polynomials
| Autor: | Łukasz Pańkowski, Adrian W. Dudek, Victor Scharaschkin |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Number Theory
General Mathematics Mathematics::Number Theory 010102 general mathematics Sigma Divisor function 0102 computer and information sciences Divisor (algebraic geometry) 01 natural sciences 11A25 11C08 Combinatorics Number theory Quadratic equation Integer 010201 computation theory & mathematics FOS: Mathematics Asymptotic formula Number Theory (math.NT) 0101 mathematics Mathematics |
| ISSN: | 0004-9727 |
| DOI: | 10.48550/arxiv.1806.01404 |
| Popis: | Lapkova [‘On the average number of divisors of reducible quadratic polynomials’, J. Number Theory 180 (2017), 710–729] uses a Tauberian theorem to derive an asymptotic formula for the divisor sum $\sum _{n\leq x}d(n(n+v))$ where $v$ is a fixed integer and $d(n)$ denotes the number of divisors of $n$. We reprove this result with additional terms in the asymptotic formula, by investigating the relationship between this divisor sum and the well-known sum $\sum _{n\leq x}d(n)d(n+v)$. |
| Databáze: | OpenAIRE |
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