Square-Free Integers as Ideal Norms

Square-Free Integers as Ideal Norms

Elaborating on Katzel＇s result, Zhai obtained a sharp short interval result for the number of ways of expressing a square-free integer as sums of two squares. In this note we view Zhai＇s decom- position as one by degree 1 prime ideals in the Gaussian field and extend Zhai＇s approach to a wider range...

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Veröffentlicht in:Acta mathematica Sinica. English series 2010-04, Vol.26 (4), p.621-628
Hauptverfasser: Kanemitsu, Shigeru, Laurinčikas, Antanas, Ma, Jing
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Conformity
Decomposition
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Normal distribution
Norms
Studies
二次域
平方和
素理想
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Beschreibung
Zusammenfassung:Elaborating on Katzel＇s result, Zhai obtained a sharp short interval result for the number of ways of expressing a square-free integer as sums of two squares. In this note we view Zhai＇s decom- position as one by degree 1 prime ideals in the Gaussian field and extend Zhai＇s approach to a wider range of quadratic fields etc.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-010-8450-7