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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Partitions of totally positive elements in real quadratic fields
 Stern, David ; Kala, Vítězslav (advisor) ; Gil Muñoz, Daniel (referee)
We consider the additive semigroup O+ K(+) of totally positive integers in a real quadratic field K = Q( √ D). We define on O+ K(+) the partition function pK(α) and de- velop an algorithm for computing pK(α) for different square-free D and different α ∈ O+ K. We then investigate the behaviour of pK(α), characterizing the square-free numbers D for which pK(α) attains the numbers 1 through 5. Finally, we prove a sufficient condition for the number 6 to be attainable by pK(α). 1
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Subfields of number field extensions and quadratic forms
 Doležálek, Matěj ; Kala, Vítězslav (advisor) ; Gil Muñoz, Daniel (referee)
A number of recent results give constructions of totally real number fields of specific degrees that do not admit universal quadratic forms of small rank. Given a totally real number field L that is known to have a certain lower bound on the rank of universal quadratic forms, one may try to construct extensions of L that also satisfy this bound. In this thesis, we present a way of constructing such an extension as the compositum of L and some suitable number field K. The construction relies on inequalities involving traces and discriminants in number fields and controlling the subfields of KL using Galois correspondence, which then leads to examining subgroups in direct products of groups. 1
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