Class numbers of orders in quartic fields [Elektronische Ressource] / vorgelegt von Mark Pavey

Class Numbers of OrdersinQuartic FieldsDissertationder Fakult˜ at fur˜ Mathematik und Physikder Eberhard-Karls-Universit˜ at Tubingen˜zur Erlangung des Grades eines Doktors der Naturwissenschaftenvorgelegt vonMark Paveyaus Cheltenham Spa, UK2006Mundliche Prufung:˜ 11.05.2006Dekan: Prof.Dr.P.Schmid1.Berichterstatter: Prof.Dr.A.Deitmar2.Berich Prof.Dr.J.HausenDedicated to my parents:Deryk and Frances Pavey,who have always supported me.AcknowledgmentsFirst of all thanks must go to my doctoral supervisor Professor Anton Deit-mar, without whose enthusiasm and unfailing generosity with his time andexpertise this project could not have been completed.The flrst two years of research for this project were undertaken at ExeterUniversity, UK, with funding from the Engineering and Physical Sciences Re-search Council of Great Britain (EPSRC). I would like to thank the membersof the Exeter Maths Department and EPSRC for their support. Likewise Ithank the members of the Mathematisches Institut der Universit˜ at Tubingen,˜where the work was completed.Finally, I wish to thank all the family and friends whose friendship andencouragement have been invaluable to me over the last four years. I haveto mention particularly the Palmers, the Haywards and my brother Phill inSeaton, and those who studied and drank alongside me: Jon, Pete, Dave,Ralph, Thomas and the rest.