On the surjectivity of Galois representations attached to elliptic curves over number fields
Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.
Let K = Q(ζ) and let h be its class number. Kummer showed that p divides h if and only if p divides the numerator of some Bernoulli number. In this expository note we discuss the generalizations of this type of criterion to totally real fields and quadratic imaginary fields.
On certain closed subgroups of .
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