Fields with minimal discriminants : an empirical study
Modern algebra is a ubiquitous topic within mathematics and has many large and interconnected branches. Within algebra there is a branch known as field theory. Two measures of the complexity of a number field are its discriminant and signature. This paper correlates these two measures for fields of...
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| Format: | Others |
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2011
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| Online Access: | http://cardinalscholar.bsu.edu/handle/handle/187968 http://liblink.bsu.edu/uhtbin/catkey/1314333 |
| Summary: | Modern algebra is a ubiquitous topic within mathematics and has many large and interconnected branches. Within algebra there is a branch known as field theory. Two measures of the complexity of a number field are its discriminant and signature. This paper correlates these two measures for fields of degree 4— 8 for which the discriminant is as small as possible. In studying the different ways minimal discriminants were located, an exponential relationship was noticed between the absolute value of the minimal discriminant and the signature. The actual absolute minimal discriminants and the exponential trends were then compared to and consistent with lower bounds for the absolute minimal discriminants previously estimated by Andrew Odlyzko. As the area becomes more saturated with computational findings, relating newly-discovered facts to previous estimates is useful for refining current estimates and generating new conjectures. === Department of Mathematical Sciences |
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