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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Composition of quadratic forms over number fields
 Zemková, Kristýna ; Kala, Vítězslav (advisor) ; Francírek, Pavel (referee)
The thesis is concerned with the theory of binary quadratic forms with coefficients in the ring of algebraic integers of a number field. Under the assumption that the number field is of narrow class number one, there is developed a theory of composition of such quadratic forms. For a given discriminant, the composition is determined by a bijection between classes of quadratic forms and a so-called relative oriented class group (a group closely related to the class group). Furthermore, Bhargava cubes are generalized to cubes with entries from the ring of algebraic integers; by using the composition of quadratic forms, the composition of Bhargava cubes is proved in the generalized case. 1
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Bernoulli numbers and regular primes
 Le, Anh Dung ; Kala, Vítězslav (advisor) ; Vávra, Tomáš (referee)
The aim of this work is to study the relation between regular primes and regular Bernoulli numbers (or just simply Bernoulli numbers). By the class number formula we connect the class number to the values of Dirichlet L-series. We then compute certain values of Dirichlet L-series in terms of generalized Bernoulli numbers. In order to investigate the relations between two types of Bernoulli numbers we define the p-adic Dirichlet L-series. In the end we get a congruence between the class number and Bernoulli numbers modulo p. Since the regular primes are those which divide the corresponding class numbers this is precisely our goal. 1
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