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The Piltz divisor problem in number fields using the resonance method.

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Title: The Piltz divisor problem in number fields using the resonance method.
Authors: Karak, Nilmoni1 (AUTHOR) nilmonikarak@gmail.com, Mahatab, Kamalakshya1 (AUTHOR) kamalakshya@maths.iitkgp.ac.in
Source: Journal of Number Theory. Apr2026, Vol. 281, p726-740. 15p.
Subjects: Algebraic fields, Small divisors, Mathematical formulas, Mathematicians, Approximation error, Asymptotic expansions
Abstract: The Piltz divisor problem is a natural generalization of the classical Dirichlet divisor problem. In this paper, we study this problem over number fields and obtain improved Ω-bounds for its error terms. Our approach involves generalizing a Voronoi-type formula due to Soundararajan in the number field setting, and applying a recent result due to the second author. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 189762273
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: The Piltz divisor problem in number fields using the resonance method.
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  Data: <searchLink fieldCode="AR" term="%22Karak%2C+Nilmoni%22">Karak, Nilmoni</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nilmonikarak@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Mahatab%2C+Kamalakshya%22">Mahatab, Kamalakshya</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kamalakshya@maths.iitkgp.ac.in</i>
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  Data: <searchLink fieldCode="DE" term="%22Algebraic+fields%22">Algebraic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Small+divisors%22">Small divisors</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+formulas%22">Mathematical formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematicians%22">Mathematicians</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+expansions%22">Asymptotic expansions</searchLink>
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  Label: Abstract
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  Data: The Piltz divisor problem is a natural generalization of the classical Dirichlet divisor problem. In this paper, we study this problem over number fields and obtain improved Ω-bounds for its error terms. Our approach involves generalizing a Voronoi-type formula due to Soundararajan in the number field setting, and applying a recent result due to the second author. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jnt.2025.10.013
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 15
        StartPage: 726
    Subjects:
      – SubjectFull: Algebraic fields
        Type: general
      – SubjectFull: Small divisors
        Type: general
      – SubjectFull: Mathematical formulas
        Type: general
      – SubjectFull: Mathematicians
        Type: general
      – SubjectFull: Approximation error
        Type: general
      – SubjectFull: Asymptotic expansions
        Type: general
    Titles:
      – TitleFull: The Piltz divisor problem in number fields using the resonance method.
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            NameFull: Karak, Nilmoni
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            NameFull: Mahatab, Kamalakshya
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          Dates:
            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
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              Value: 281
          Titles:
            – TitleFull: Journal of Number Theory
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