Author:
Kim Kwang-Seob,König Joachim
Abstract
Abstract
Let
$n$
be an integer congruent to
$0$
or
$3$
modulo
$4$
. Under the assumption of the ABC conjecture, we prove that, given any integer
$m$
fulfilling only a certain coprimeness condition, there exist infinitely many imaginary quadratic fields having an everywhere unramified Galois extension of group
$A_n \times C_m$
. The same result is obtained unconditionally in special cases.
Publisher
Cambridge University Press (CUP)
Reference24 articles.
1. Some results on the Mordell-Weil group of the Jacobian of the Fermat curve;Gross;Invent. Math.,1978
2. Unramified extensions over low degree number fields;König;J. Number Theory,2020
3. Unramified extensions of quadratic number fields, II;Uchida;Tohoku Math. J.,1970
4. Divisibility of class numbers of imaginary quadratic fields;Soundararajan;J. Lond. Math. Soc.,2000