Either by signing into your account or linking your membership details before your order is placed. Your points will be added to your account once your order is shipped. Click on the cover image above to read some pages of this book! Andrews conferencein Ithasbecomearichtheoryrequiringtoolsfromandhaving applications to many areas of group theory. Indeed, much of this progress is 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?
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? First, there are now numerous calculations of zeta functions of groups by doctoralstudentsofthe?
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. In particular, we document the functional equations frequently satis? Explaining this phenomenon is, according to the?
It also contains a large number of examples of groups for which these zeta functions were explicitly computed. These surely will be valuable for inspiring further developments. The book will be not only a valuable reference for people working in this area, but also a fascinating reading for everybody who wants to understand the role zeta functions have in group theory and the connections between subgroup growth and algebraic geometry over finite fields revealed by this theory.
Baxa, Monatshefte fur Mathematik, Vol. Segal, and G.
Subgroups of finite index in nilpotent groups. Hrushovski, B. Martin, S. Rideau, and R. Definable equivalence relations and zeta functions of groups, arXiv:.
Zeta function of representations of compact p-adic analytic groups. Pure Math. Representation growth and representation zeta functions of groups, Note Mat. Klopsch, N.
Nikolov, and C. Larsen and A. Representation growth of linear groups, J. Eur Math. JEMS 10 , no. Liebeck and A. Character degrees and random walks in finite groups of Lie type, Proc. Counting subrings of Zn of index k, J. Combin Theory Ser. A , no.
Functional equations for zeta functions of groups and rings - Dimensions
Lubotzky and A. Varieties of representations of finitely generated groups, Mem. Lubotzky, A. Mann, and D.
- The definition of good.
- A newcomer's guide to zeta functions of groups and rings;
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Finitely generated groups of polynomial subgroup growth Lubotzky and B. Polynomial representation growth and the congruence subgroup growth. Lubotzky and D. Schriften, vol. Orders of a quartic field, Mem. Nunley and A. Simple representations of the integral Heisenberg group. Zeta, version 0. Computing topological zeta functions of groups, algebras, and modules, I. Computing topological zeta functions of groups, algebras, and modules, II. Schein and C. Normal zeta functions of the Heisenberg groups over number rings I - the unramified case, , to appear in J.
London Math Soc. Israel J. Normal zeta functions of the Heisenberg groups over number rings II - the non-split case, , to appear in.
Zeta functions of groups and rings
Zeta functions of groups and rings, Ph. Pure Appl. Stasinski and C. Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B. Functional equations for local normal zeta functions of nilpotent groups, Geom.