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Weber’s class invariants. (English) Zbl 0226.12005
The author considers problems related to Gauss’ “10th discriminant problem”. He makes use of theorems of class field theory and establishes in this way, for instance, Heegner’s unproved assertions because of which K. Heegner’s work [Math. Z. 56, 227–253 (1952; Zbl 0049.16202)] was at first disbelieved.
The author also introduces new points of view to questions which recently have been considered, for instance, by A. Baker [Mathematika 13, No. 2, 204–216 (1966; Zbl 0161.05201)], K. Ramachandra [Ann. Math. (2) 80, 104–148 (1964; Zbl 0142.29804)] and H. M. Stark [Mich. Math. J. 14, 1–27 (1967; Zbl 0148.27802)] and he gives a good summary of the results of this field.

MSC:
11R29 Class numbers, class groups, discriminants
11R37 Class field theory
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