Thestudyofthesubgroupgrowthofin?nitegroupsisanareaofmathematical research that has grown rapidly since its inception at the Groups St. Andrews conferencein1985.Ithasbecomearichtheoryrequiringtoolsfromandhaving applications to many areas of group theory. Indeed, much of this progress i... s chronicled by Lubotzky and Segal within their book . However, one area within this study has grown explosively in the last few years. This is the study of the zeta functions of groups with polynomial s- groupgrowth,inparticularfortorsion-free?nitely-generatednilpotentgroups. These zeta functions were introduced in , and other key papers in the - velopment of this subject include [10, 17], with [19, 23, 15] as well as  presenting surveys of the area. The purpose of this book is to bring into print signi?cant and as yet unpublished work from three areas of the theory of zeta functions of groups. First, there are now numerous calculations of zeta functions of groups by doctoralstudentsofthe?rstauthorwhichareyettobemadeintoprintedform outside their theses. These explicit calculations provide evidence in favour of conjectures, or indeed can form inspiration and evidence for new conjectures. We record these zeta functions in Chap.2. In particular, we document the functional equations frequently satis?ed by the local factors. Explaining this phenomenon is, according to the ?rst author and Segal , 'one of the most intriguing open problems in the area'.
OBS! E-bogen kan ikke læses på Kindle eller i iBooks. Du kan læse e-bogen på computer, tablet, smartphone og diverse e-bogslæsere. Du skal bruge et specielt læseprogram til din enhed. Læs mere om programmer, sidetal og print af e-bøger her.
Hvis denne bog ikke er noget for dig, kan du benytte kategorierne nedenfor til at finde andre titler. Klik på en kategori for at se lignende bøger.