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Generalizing the theorem of Nakagawa on binary cubic forms to number fields
(2012-07)
The goal of this thesis is to study possible generalizations of a theorem of Nakagawa, first stated as a conjecture by Ohno, that gives a relationship between cubic fields of positive and negative discriminant. This theorem ...
Asymptotics of class number and genus for abelian extensions of an algebraic function field
(2012-05)
Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established. The proof is completely classical, employing well-known results from congruence function field theory.