LMS Durham Symposium on Computational Number Theory
24 July - 3 August 2000

Explicit construction of number field extensions of small degree, with applications to discriminant counting

(Two talks)

Henri COHEN (Bordeaux)

Abstract: After reviewing some results coming from Class Field Theory and the theory of higher ramification groups, we show how to construct explicitly extensions of number fields of type C_l, D_l, A_4 and S_4 (l prime). We deduce from this both asymptotic and exact formulas for the number of such extensions. For absolute extensions, we explain some elementary number-theoretical methods which have allowed us to count the number of desired extensions up to very high discriminant (10^{37} in the best case C_3).

This is joint work with F. Diaz y Diaz and M. Olivier.

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