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Brigham Young University
Math Department

Darrin Doud

314 TMCB
Department of Mathematics
Brigham Young University
Provo, UT 84602

phone:(801)422-1204
fax:(801)422-0504
e-mail:doud@math.byu.edu

Local corrections of discriminant bounds and small degree extensions of quadratic base fields

with Sharon Brueggemn
in review.

Abstract: Using analytic techniques of Odlyzko and Poitou, we create tables of lower bounds for discriminants of number fields, including local corrections for ideals of known norm. Comparing the lower bounds found in these tables with upper bounds on discriminants of number fields obtained from calculations involving differents, we prove the nonexistence of a number of small degree extensions of quadratic fields having limited ramification. We note that several of our results require the locally corrected bounds.

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DVI PDF PS

Supplementary Tables and Computer Code

In addition to a preprint of our paper, we also make available further tables of discriminant bounds involving local corrections as well as the Maple code used to construct the tables. These tables consist of unconditional lower bounds for discriminants of number fields of a given degree, with r1 real places and primes of certain norms. For details about the tables and their construction see the paper. We plan to include more bounds derived under the assumption of the GRH in the near future.
Unconditional BoundsBounds requiring GRH
Degree 5 Degree 5 (GRH)
Degree 6 Degree 6 (GRH)
Degree 7 Degree 7 (GRH)
Degree 8 Degree 8 (GRH)
Degree 9 Degree 9 (GRH)
Degree 10 Degree 10 (GRH)
Degree 11 Degree 11 (GRH)
Degree 12 Degree 12 (GRH)
Degree 13 Degree 13 (GRH)
Degree 14 Degree 14 (GRH)
Degree 15 Degree 15 (GRH)
Degree 16 Degree 16 (GRH)
Degree 17 Degree 17 (GRH)
Degree 18 Degree 18 (GRH)
Degree 19
Degree 20
Degree 22
Degree 24
Degree 25
Degree 26
To download maple code, right click on the links below, and save the file to load into Maple

Maple Code for unconditional case

Maple Code for GRH case (totally complex)

Maple Code for GRH case (two real embeddings)

Maintained by Darrin Doud.

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