Darrin Doud
322 TMCB Department of Mathematics Brigham Young University Provo, UT 84602   phone:  (801)4221204 
fax:  (801)4220504  email:  

Local corrections of discriminant bounds and small degree extensions of quadratic base fields
with Sharon Brueggeman
International Journal of Number Theory, 4(2008), 349361.
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.
Download
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 r
_{1} real places and primes of certain norms. For details about the tables and their construction see the
paper.
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)
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 Benjamin Linowitz, Selectivity in central simple algebras and isospectrality, Ph.D. Thesis, Dartmouth College, 2012
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 Benjamin Linowitz, D. B. McReynolds, Paul Pollack, and Lola Thompson, Counting and effective rigidity in algebra and geometry, ArXiv preprint, (2014).