Zeta Functions of Groups and Rings
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 is chronicled by Lubotzky and Segal within their book [42]. 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 [32], and other key papers in the - velopment of this subject include [10, 17], with [19, 23, 15] as well as [42] 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 The purpose of this book is to bring into print signi?cant and as yet unpublished work from three areas of the theory of zeta functions of groups.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 [23], “one of the most intriguing open problems in the area”.
Mathematics & StatisticsPost-CalculusAbstract AlgebraNumber Theory
RELEASED2007
PUBLISHERSpringer Nature
LENGTH212
LANGUAGEENGLISH
Marcus du Sautoy is the Charles Simonyi Professor for the Public Understanding of Science at the Oxford University, a chair he holds jointly at the Department of Continuing Education and the Mathematical Institute. He is also a Professor of Mathematics and a Fellow of New College. He was made a Fellow of the Royal Society in 2016. In 2001 he won the prestigious Berwick Prize of the London Mathematical Society awarded every two years to reward the best mathematical research made by a mathematician under 40. In 2004 Esquire Magazine chose him as one of the 100 most influential people under 40 in Britain and in 2008 he was included in the prestigious directory Who’s Who. In 2009 he was awarded the Royal Society’s Faraday Prize, the UK’s premier award for excellence in communicating science. He received an OBE for services to science in the 2010 New Year’s Honours List. He also received the Joint Policy for Mathematics Board Communications Award for 2010 and the London Mathematical Society Zeeman Medal for 2014 for promotion of mathematics to the public. -- [(Source)](https://www.simonyi.ox.ac.uk/about-marcus/)
Zeta Functions of Groups and Rings
by Marcus du Sautoy, Luke Woodward
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 is chronicled by Lubotzky and Segal within their book [42]. 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 [32], and other key papers in the - velopment of this subject include [10, 17], with [19, 23, 15] as well as [42] 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 [23], “one of the most intriguing open problems in the area”.
Mathematics & StatisticsPost-CalculusAbstract AlgebraNumber Theory
RELEASED2007
PUBLISHERSpringer Nature
LENGTH212
LANGUAGEENGLISH
Marcus du Sautoy is the Charles Simonyi Professor for the Public Understanding of Science at the Oxford University, a chair he holds jointly at the Department of Continuing Education and the Mathematical Institute. He is also a Professor of Mathematics and a Fellow of New College. He was made a Fellow of the Royal Society in 2016. In 2001 he won the prestigious Berwick Prize of the London Mathematical Society awarded every two years to reward the best mathematical research made by a mathematician under 40. In 2004 Esquire Magazine chose him as one of the 100 most influential people under 40 in Britain and in 2008 he was included in the prestigious directory Who’s Who. In 2009 he was awarded the Royal Society’s Faraday Prize, the UK’s premier award for excellence in communicating science. He received an OBE for services to science in the 2010 New Year’s Honours List. He also received the Joint Policy for Mathematics Board Communications Award for 2010 and the London Mathematical Society Zeeman Medal for 2014 for promotion of mathematics to the public. -- [(Source)](https://www.simonyi.ox.ac.uk/about-marcus/)
