LOCAL CORRECTIONS OF DISCRIMINANT BOUNDS AND SMALL DEGREE EXTENSIONS OF QUADRATIC BASE FIELDS
Sharon Brueggeman, Darrin Doud · International Journal of Number Theory · 2008
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.