Multiplicative functions over the Gaussian integers. II (Q1091415)
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scientific article; zbMATH DE number 4010590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplicative functions over the Gaussian integers. II |
scientific article; zbMATH DE number 4010590 |
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Multiplicative functions over the Gaussian integers. II (English)
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1986
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The authors continue their study of multiplicative functions on the group \(G^*\) of integers of \(\mathbb Q(i)\setminus \{0\}\) [ibid. 48, 187--190 (1986; Zbl 0615.10010)]. In particular, conditions are given under which such a function \(F\) is of the form \(F(\alpha)=| \alpha |^s e^{ik \arg \alpha}\) \((s\in\mathbb C\), \(k\in\mathbb Z\), \(0\leq \text{Re}\, s<1)\). (Remark. In Lemma 1 read \(\mathfrak B=G^*\) instead of \(\beta =G^*\).)
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Gaussian integers
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completely multiplicative functions
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regularity condition
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0.8529012203216553
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0.7890335321426392
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0.7750369310379028
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