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University of Toronto
1. Dahl, Alexander Oswald. On Moments of Class Numbers of Real Quadratic Fields.
Degree: 2010, University of Toronto
Class numbers of algebraic number fields are central invariants. Once the underlying field has an infinite unit group they behave very irregularly due to a non-trivial regulator. This phenomenon occurs already in the simplest case of real quadratic number fields of which very little is known. Hooley derived a conjectural formula for the average of class numbers of real quadratic fields. In this thesis we extend his methods to obtain conjectural formulae and bounds for any moment, i.e., the average of an arbitrary real power of class numbers. Our formulae and bounds are based on similar (quite reasonable) assumptions of Hooley's work. In the final chapter we consider the case of the -1 power from a numerical point of view and develop an efficient algorithm to compute the average for the -1 class number power without computing class numbers.
MASTAdvisors/Committee Members: Blomer, Valentin, Mathematics.
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APA (6th Edition):
Dahl, A. O. (2010). On Moments of Class Numbers of Real Quadratic Fields. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/24553
Chicago Manual of Style (16th Edition):
Dahl, Alexander Oswald. “On Moments of Class Numbers of Real Quadratic Fields.” 2010. Masters Thesis, University of Toronto. Accessed July 15, 2020. http://hdl.handle.net/1807/24553.
MLA Handbook (7th Edition):
Dahl, Alexander Oswald. “On Moments of Class Numbers of Real Quadratic Fields.” 2010. Web. 15 Jul 2020.
Dahl AO. On Moments of Class Numbers of Real Quadratic Fields. [Internet] [Masters thesis]. University of Toronto; 2010. [cited 2020 Jul 15]. Available from: http://hdl.handle.net/1807/24553.
Council of Science Editors:
Dahl AO. On Moments of Class Numbers of Real Quadratic Fields. [Masters Thesis]. University of Toronto; 2010. Available from: http://hdl.handle.net/1807/24553