Weber’s class invariants. (English) Zbl 0226.12005

Birch, B. J.

Mathematika 16, 283-294 (1969).

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.

Reviewer: Timo Lepistö (Tampere)

MSC:

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

Keywords:

10th discriminant problem; Gauss; Heegner; Baker; Ramachandra; Stark

Citations:

Zbl 0049.16202; Zbl 0161.05201; Zbl 0142.29804; Zbl 0148.27802

References:

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