Geodesic
Ramified Characters of Id\`ele Groups of One-Class Quadratic Fields
Informatics and Automation, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 122-129.

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The necessary and sufficient conditions for the triviality of the ramified characters of the idèle group $A_d^\times $ of a one-class quadratic field $\mathbb Q(\sqrt d)$ on its multiplicative group $\mathbb Q^\times(\sqrt d)$ are established; i.e., the characters of the group $A_d^\times/\mathbb Q^\times(\sqrt d)$ are completely described. 
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V. S. Vladimirov. Ramified Characters of Id\`ele Groups of One-Class Quadratic Fields. Informatics and Automation, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 122-129. http://geodesic.mathdoc.fr/item/TRSPY_1999_224_a6/

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