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Stability results for local zeta functions of groups and related structures
- Publication Year :
- 2015
-
Abstract
- Various types of local zeta functions studied in asymptotic group theory admit two natural operations: (1) change the prime and (2) perform local base extensions. Often, the effects of both of these operations can be expressed simultaneously in terms of a single explicit formula. We show that in these cases, the behaviour of local zeta functions under variation of the prime in a set of density 1 in fact completely determines these functions for almost all primes and, moreover, it also determines their behaviour under local base extensions. We discuss applications to topological zeta functions, functional equations, and questions of uniformity.<br />Comment: 15 pages
- Subjects :
- Mathematics - Group Theory
Mathematics - Number Theory
11M41, 20F69
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1504.04164
- Document Type :
- Working Paper