### Abstract

Consider the divisor sum (Formula presented.) for integers b and c. We improve the explicit upper bound of this average divisor sum in certain cases, and as an application, we give an improvement in the maximal possible number of (Formula presented.)-quadruples. The new tool is a numerically explicit Pólya–Vinogradov inequality, which has not been formulated explicitly before but is essentially due to Frolenkov–Soundararajan.

Original language | English |
---|---|

Pages (from-to) | 675–678 |

Number of pages | 4 |

Journal | Monatshefte fur Mathematik |

Volume | 186 |

Issue number | 4 |

Publication status | Published - 24 Mar 2018 |

### Fingerprint

### Keywords

- Character sums
- Number of divisors
- Quadratic polynomial

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Correction to "Explicit upper bound for the average number of divisors of irreducible quadratic polynomials".** / Lapkova, Kostadinka.

Research output: Contribution to journal › Article › Research › peer-review

*Monatshefte fur Mathematik*, vol. 186, no. 4, pp. 675–678.

}

TY - JOUR

T1 - Correction to "Explicit upper bound for the average number of divisors of irreducible quadratic polynomials"

AU - Lapkova, Kostadinka

PY - 2018/3/24

Y1 - 2018/3/24

N2 - Consider the divisor sum (Formula presented.) for integers b and c. We improve the explicit upper bound of this average divisor sum in certain cases, and as an application, we give an improvement in the maximal possible number of (Formula presented.)-quadruples. The new tool is a numerically explicit Pólya–Vinogradov inequality, which has not been formulated explicitly before but is essentially due to Frolenkov–Soundararajan.

AB - Consider the divisor sum (Formula presented.) for integers b and c. We improve the explicit upper bound of this average divisor sum in certain cases, and as an application, we give an improvement in the maximal possible number of (Formula presented.)-quadruples. The new tool is a numerically explicit Pólya–Vinogradov inequality, which has not been formulated explicitly before but is essentially due to Frolenkov–Soundararajan.

KW - Character sums

KW - Number of divisors

KW - Quadratic polynomial

UR - http://www.scopus.com/inward/record.url?scp=85044358293&partnerID=8YFLogxK

M3 - Article

VL - 186

SP - 675

EP - 678

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

SN - 0026-9255

IS - 4

ER -