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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/24553

Title: On Moments of Class Numbers of Real Quadratic Fields
Authors: Dahl, Alexander Oswald
Advisor: Blomer, Valentin
Department: Mathematics
Keywords: analytic number theory
real quadratic fields
binary quadratic forms
class group moments
Issue Date: 22-Jul-2010
Abstract: 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.
URI: http://hdl.handle.net/1807/24553
Appears in Collections:Master
Department of Mathematics - Master theses

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