TY - BOOK AU - AU - ED - SpringerLink (Online service) TI - Zeta Functions of Groups and Rings T2 - Lecture Notes in Mathematics, SN - 9783540747765 AV - QA174-183 U1 - 512.2 23 PY - 2008/// CY - Berlin, Heidelberg PB - Springer Berlin Heidelberg KW - Mathematics KW - Group theory KW - Algebra KW - Number theory KW - Group Theory and Generalizations KW - Number Theory KW - Non-associative Rings and Algebras N1 - Nilpotent Groups: Explicit Examples -- Soluble Lie Rings -- Local Functional Equations -- Natural Boundaries I: Theory -- Natural Boundaries II: Algebraic Groups -- Natural Boundaries III: Nilpotent Groups; ZDB-2-SMA; ZDB-2-LNM N2 - Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation UR - http://dx.doi.org/10.1007/978-3-540-74776-5 ER -