test Browse by Author Names Browse by Titles of Works Browse by Subjects of Works Browse by Issue Dates of Works
       

Advanced Search
Home   
 
Browse   
Communities
& Collections
  
Issue Date   
Author   
Title   
Subject   
 
Sign on to:   
Receive email
updates
  
My Account
authorized users
  
Edit Profile   
 
Help   
About T-Space   

T-Space at The University of Toronto Libraries >
School of Graduate Studies - Theses >
Master >

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

Files in This Item:

File Description SizeFormat
Dahl_Alexander_O_201006_MSc_thesis.pdf343.95 kBAdobe PDF
View/Open

Items in T-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

uoft