Vol. 311, No. 2, 2021

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Correction to the article Uniform bounds of the Piltz divisor problem over number fields

Wataru Takeda

Vol. 311 (2021), No. 2, 505–509

Correction to Pacific Journal of Mathematics 301:2 (2019) 601–616

Abstract

The article in question gave an upper bound for the Piltz divisor problem over number fields, using estimates of exponential sums. It contained some mistakes. Here we correct these inaccurate claims and give a uniform upper bound for the Piltz divisor problem.

Keywords
ideal counting function, exponential sum, Piltz divisor problem
Mathematical Subject Classification
Primary: 11N37
Secondary: 11R42
Milestones
Received: 1 August 2020
Revised: 9 August 2020
Accepted: 13 August 2020
Published: 31 July 2021
Authors
Wataru Takeda
Department of Mathematics
Nagoya University
Chikusa-ku
Nagoya 464-8602
Japan