LOCAL CORRECTIONS OF DISCRIMINANT BOUNDS AND SMALL DEGREE EXTENSIONS OF QUADRATIC BASE FIELDS

Autor:	Darrin Doud, Sharon Brueggeman
Rok vydání:	2008
Předmět:	Discrete mathematics Algebra and Number Theory Quadratic equation Discriminant Norm (mathematics) Algebraic number field Mathematics
Zdroj:	International Journal of Number Theory. :349-361
ISSN:	1793-7310 1793-0421
DOI:	10.1142/s1793042108001389
Popis:	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.
Databáze:	OpenAIRE
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