Academic Journal

On an upper bound for biquadratic Weyl sums

Bibliographic Details
Title: On an upper bound for biquadratic Weyl sums
Authors: Deshouillers, Jean-Marc
Publisher Information: Scuola Normale Superiore, Pisa
Subject Terms: estimation of sums over multiplicative functions in residue classes, Hardy-Littlewood method, Waring problem for biquadrates, Asymptotic results on arithmetic functions, Waring's problem and variants, Estimates on exponential sums, estimates of exponential sums with explicit constants
Description: In order to solve the Waring problem for biquadrates \((g(4)=19)\) it is unavoidable to apply the Hardy-Littlewood method with explicit \(O\)- constants in the error terms. In the paper under review the author proves an explicit estimation for the exponential sum \[ S_ \varepsilon= \sum_{P-{1\over 2}\varepsilon10^{80}\), \(0
Document Type: Article
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Access URL: https://zbmath.org/165239
Accession Number: edsair.c2b0b933574d..0f0861d63daccda7b2abc3b37b5c24e8
Database: OpenAIRE
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PubType: Academic Journal
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  Data: On an upper bound for biquadratic Weyl sums
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  Data: <searchLink fieldCode="AR" term="%22Deshouillers%2C+Jean-Marc%22">Deshouillers, Jean-Marc</searchLink>
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  Data: Scuola Normale Superiore, Pisa
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  Data: <searchLink fieldCode="DE" term="%22estimation+of+sums+over+multiplicative+functions+in+residue+classes%22">estimation of sums over multiplicative functions in residue classes</searchLink><br /><searchLink fieldCode="DE" term="%22Hardy-Littlewood+method%22">Hardy-Littlewood method</searchLink><br /><searchLink fieldCode="DE" term="%22Waring+problem+for+biquadrates%22">Waring problem for biquadrates</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+results+on+arithmetic+functions%22">Asymptotic results on arithmetic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Waring's+problem+and+variants%22">Waring's problem and variants</searchLink><br /><searchLink fieldCode="DE" term="%22Estimates+on+exponential+sums%22">Estimates on exponential sums</searchLink><br /><searchLink fieldCode="DE" term="%22estimates+of+exponential+sums+with+explicit+constants%22">estimates of exponential sums with explicit constants</searchLink>
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  Data: In order to solve the Waring problem for biquadrates \((g(4)=19)\) it is unavoidable to apply the Hardy-Littlewood method with explicit \(O\)- constants in the error terms. In the paper under review the author proves an explicit estimation for the exponential sum \[ S_ \varepsilon= \sum_{P-{1\over 2}\varepsilon10^{80}\), \(0
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    Subjects:
      – SubjectFull: estimation of sums over multiplicative functions in residue classes
        Type: general
      – SubjectFull: Hardy-Littlewood method
        Type: general
      – SubjectFull: Waring problem for biquadrates
        Type: general
      – SubjectFull: Asymptotic results on arithmetic functions
        Type: general
      – SubjectFull: Waring's problem and variants
        Type: general
      – SubjectFull: Estimates on exponential sums
        Type: general
      – SubjectFull: estimates of exponential sums with explicit constants
        Type: general
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      – TitleFull: On an upper bound for biquadratic Weyl sums
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