Computing class numbers of orders in imaginary quadratic fields

Dogger, Floor (2019) Computing class numbers of orders in imaginary quadratic fields. Bachelor's Thesis, Mathematics.

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Abstract

The connection between binary quadratic forms and imaginary quadratic number fields is studied with the aim of computing class numbers of orders in imaginary quadratic fields. The form class group is constructed and we define the Dirichlet composition of two primitive positive definite forms of the same discriminant. We prove in detail that the operation induced by Dirichlet composition is well-defined and provides an Abelian structure on the form class group. Algorithms to compute the class number of the form class group are implemented in Sage. The construction of the ideal class group is discussed next. We prove that every form class group is isomorphic to an ideal class group of a unique order in an imaginary quadratic field. The implemented algorithms are used to compute class numbers of orders in imaginary quadratic fields. We finish with computing class numbers of the ring of integers in imaginary quadratic fields to check whether they are unique factorization domains.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Kilicer, P.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	12 Jul 2019
Last Modified:	16 Jul 2019 12:29
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/20175

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