Zeta functions of groups and rings – functional equations and analytic uniformity

2019 ◽  
pp. 345-363
Author(s):  
Christopher Voll
Keyword(s):  
Functional Equations ◽  
Zeta Functions ◽  
Zeta Functions Of Groups

Stability results for local zeta functions of groups algebras, and modules

2017 ◽  
Vol 165 (3) ◽  
pp. 435-444 ◽  
Author(s):  
TOBIAS ROSSMANN
Keyword(s):  
Group Theory ◽  
Functional Equations ◽  
Zeta Functions ◽  
Local Zeta Functions ◽  
Single Formula ◽  
Almost All ◽  
Stability Results ◽  
Zeta Functions Of Groups ◽  
Local Base

AbstractVarious 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 the preceding operations can be expressed simultaneously in terms of a single formula, a statement made precise using what we call local maps of Denef type. We show that assuming the existence of such formulae, 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.

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