28 citations · 121 across the 52 of their papers we have counts for
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Imaginary quadratic fields with Cl_2(k) = (2,2,2)
Elliot Benjamin, Franz Lemmermeyer, Chip Snyder
In this article we classify the complex quadratic number fields k with 2-class group of type (2,2,2) whose Hilbert 2-class fields have a 2-class group of rank 2, and then determine…
The development of the princial genus theorem
Franz Lemmermeyer
In this article we sketch the development of the principal genus theorem from its conception by Gauss in the case of binary quadratic forms to the cohomological formulation of the…
Galois action on class groups
Franz Lemmermeyer
It is well known that the Galois group of an extension puts constraints on the structure of the relative ideal class groups. Using only basic parts of the theory of group represent…
Families of noncongruent numbers
Franz Lemmermeyer
Let E_k denote the elliptic curve defined by y^2 = x(x^2 - k^2). We consider the curves with k = pl, p = l = 1 mod 8 primes, and show that the density of rank-0 curves among them i…