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Improvements on exponential sums related to Piatetski-Shapiro primes.

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Title: Improvements on exponential sums related to Piatetski-Shapiro primes.
Authors: Lu, Li1 (AUTHOR) lilu_math@foxmail.com, Guo, Lingyu1 (AUTHOR) guo.lingyu@foxmail.com, Guo, Victor Zhenyu1 (AUTHOR) guozyv@xjtu.edu.cn
Source: Journal of Number Theory. Apr2026, Vol. 281, p700-725. 26p.
Subjects: Exponential sums, Prime numbers, Number theory
Abstract: We prove a new bound to the exponential sum of the form ∑ h ∼ H δ h ∑ m ∼ M ∑ n ∼ N m n ∼ x a m b n e (α m n + h (m n + u) γ) , by a new approach to the Type I sum. The sum can be applied to many problems related to Piatetski-Shapiro primes, which are primes of the form ⌊ n c ⌋. In this paper, we improve the admissible range of the Balog-Friedlander condition, which leads to an improvement to the ternary Goldbach problem with Piatetski-Shapiro primes. We also investigate the distribution of Piatetski-Shapiro primes in arithmetic progressions, Piatetski-Shapiro primes in a Beatty sequence and so on. [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.)
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DbLabel: Engineering Source
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PubTypeId: academicJournal
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  Data: Improvements on exponential sums related to Piatetski-Shapiro primes.
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  Data: <searchLink fieldCode="AR" term="%22Lu%2C+Li%22">Lu, Li</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lilu_math@foxmail.com</i><br /><searchLink fieldCode="AR" term="%22Guo%2C+Lingyu%22">Guo, Lingyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> guo.lingyu@foxmail.com</i><br /><searchLink fieldCode="AR" term="%22Guo%2C+Victor+Zhenyu%22">Guo, Victor Zhenyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> guozyv@xjtu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Apr2026, Vol. 281, p700-725. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Exponential+sums%22">Exponential sums</searchLink><br /><searchLink fieldCode="DE" term="%22Prime+numbers%22">Prime numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink>
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  Label: Abstract
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  Data: We prove a new bound to the exponential sum of the form ∑ h ∼ H δ h ∑ m ∼ M ∑ n ∼ N m n ∼ x a m b n e (α m n + h (m n + u) γ) , by a new approach to the Type I sum. The sum can be applied to many problems related to Piatetski-Shapiro primes, which are primes of the form ⌊ n c ⌋. In this paper, we improve the admissible range of the Balog-Friedlander condition, which leads to an improvement to the ternary Goldbach problem with Piatetski-Shapiro primes. We also investigate the distribution of Piatetski-Shapiro primes in arithmetic progressions, Piatetski-Shapiro primes in a Beatty sequence and so on. [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:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.jnt.2025.10.015
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 26
        StartPage: 700
    Subjects:
      – SubjectFull: Exponential sums
        Type: general
      – SubjectFull: Prime numbers
        Type: general
      – SubjectFull: Number theory
        Type: general
    Titles:
      – TitleFull: Improvements on exponential sums related to Piatetski-Shapiro primes.
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            NameFull: Lu, Li
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            NameFull: Guo, Lingyu
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            NameFull: Guo, Victor Zhenyu
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          Dates:
            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
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              Value: 281
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            – TitleFull: Journal of Number Theory
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