177 research outputs found
Gauss periods are minimal polynomials for totally real cyclic fields of prime degree
We report extensive computational evidence that Gauss period equations are
minimal discriminant polynomials for primitive elements representing Abelian
(cyclic) polynomials of prime degrees . By computing 200 period equations up
to , we significantly extend tables in the compendious number fields
database of Kl\"uners and Malle. Up to , period equations reproduce known
results proved to have minimum discriminant. For , period
equations coincide with 53 known but unproved cases of minimum discriminant in
the database, and fill a gap of 19 missing cases. For , we
report 128 not previously known cases, 16 of them conjectured to be minimum
discriminant polynomials of Galois group . The significant advantage of
period equations is that they all may be obtained analytically using a
procedure that works for fields of arbitrary degrees, and which are extremely
hard to detect by systematic numerical search.Comment: 7 pages, 4 tables, no figure
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