Bernoulli numbers and ideal classes. (English) Zbl 1196.11145
This is a survey on the relation between the structure of the ideal class group of the cyclotomic field \(\mathbb{Q}(e^{\frac{2\pi i}{p}})\) (\(p\) prime) and divisibility properties of Bernoulli numbers. The author presents results of Kummer, Herbrand, Mazur, Wiles, Thaine, Kolyvagin and himself.
Reviewer: Florin Nicolae (Berlin)
MSC:
11R18 | Cyclotomic extensions |
11R29 | Class numbers, class groups, discriminants |
11B68 | Bernoulli and Euler numbers and polynomials |