Zeta functions of groups and rings / Marcus du Sautoy, Luke Woodward.

By: Du Sautoy, Marcus
Contributor(s): Woodward, Luke, D. Phil
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1925.Publisher: Berlin ; New York : Springer, ©2008Description: 1 online resource (xii, 208 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540747765; 3540747761; 9783540747017; 354074701X; 6611139729; 9786611139728Subject(s): Group theory | Functions, Zeta | Rings (Algebra) | Noncommutative algebras | Functions, Zeta | Group theory | Noncommutative algebras | Rings (Algebra)Genre/Form: Electronic books. Additional physical formats: Print version:: Zeta functions of groups and rings.DDC classification: 512.2 LOC classification: QA174.2 | .D8 2008ebQA3 | .L28 no. 1925Online resources: Click here to access online
Contents:
Nilpotent Groups: Explicit Examples -- Soluble Lie Rings -- Local Functional Equations -- Natural Boundaries I: Theory -- Natural Boundaries II: Algebraic Groups -- Natural Boundaries III: Nilpotent Groups.
Summary: 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.
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Includes bibliographical references (pages 201-203) and index.

Print version record.

Nilpotent Groups: Explicit Examples -- Soluble Lie Rings -- Local Functional Equations -- Natural Boundaries I: Theory -- Natural Boundaries II: Algebraic Groups -- Natural Boundaries III: Nilpotent Groups.

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.

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