We prove that the theory of the $p$-adics ${\mathbb Q}_p$ admits elimination of imaginaries provided we add a sort for ${\rm GL}_n({\mathbb Q}_p)/{\rm GL}_n({\mathbb Z}_p)$ for each $n$. We also prove that the elimination of imaginaries is uniform in $p$. Using $p$-adic and motivic integration, we deduce the uniform rationality of certain formal zeta functions arising from definable equivalence relations. This also yields analogous results for definable equivalence relations over local fields of positive characteristic. The appendix contains an alternative proof, using cell decomposition, of the rationality (for fixed $p$) of these formal zeta functions that extends to the subanalytic context. As an application, we prove rationality and u...
We study zeta functions enumerating finite-dimensional irreducible complex linear representationsof ...
AbstractA theorem of Tate and Turner says that global function fields have the same zeta function if...
A theorem of Tate and Turner says that global function fields have the same zeta function if and onl...
We prove that the theory of the p-adics Qp admits elimination of imaginaries provided we add a sort ...
© European Mathematical Society 2018. We prove that the theory of the p-adics ℚp admits elimination ...
The authors wish to thank Thomas Rohwer, Deirdre Haskell, Dugald Macpherson and Elisabeth Bouscaren ...
AbstractWe prove the rationality of the generating function associated to the number of equivalence ...
AbstractA nontrivial ring with unit eliminates imaginaries just in case its complete theory has the ...
Dung DH, Voll C. Uniform analytic properties of representation zeta functions of finitely generated ...
Recently in [4], we have investigated several zeta functions associated to finite groups and introdu...
Let G be a finitely generated nilpotent group. The representation zeta function ζG(s) of G enumerate...
We express integrals of definable functions over definable sets uniformly for non-Archimedean local ...
AbstractIt is proved that the generating function defined by the numbers of isomorphism classes of a...
This book provides a systematic account of several breakthroughs in the modern theory of zeta functi...
Stasinski A, Voll C. Representation zeta functions of nilpotent groups and generating functions for ...
We study zeta functions enumerating finite-dimensional irreducible complex linear representationsof ...
AbstractA theorem of Tate and Turner says that global function fields have the same zeta function if...
A theorem of Tate and Turner says that global function fields have the same zeta function if and onl...
We prove that the theory of the p-adics Qp admits elimination of imaginaries provided we add a sort ...
© European Mathematical Society 2018. We prove that the theory of the p-adics ℚp admits elimination ...
The authors wish to thank Thomas Rohwer, Deirdre Haskell, Dugald Macpherson and Elisabeth Bouscaren ...
AbstractWe prove the rationality of the generating function associated to the number of equivalence ...
AbstractA nontrivial ring with unit eliminates imaginaries just in case its complete theory has the ...
Dung DH, Voll C. Uniform analytic properties of representation zeta functions of finitely generated ...
Recently in [4], we have investigated several zeta functions associated to finite groups and introdu...
Let G be a finitely generated nilpotent group. The representation zeta function ζG(s) of G enumerate...
We express integrals of definable functions over definable sets uniformly for non-Archimedean local ...
AbstractIt is proved that the generating function defined by the numbers of isomorphism classes of a...
This book provides a systematic account of several breakthroughs in the modern theory of zeta functi...
Stasinski A, Voll C. Representation zeta functions of nilpotent groups and generating functions for ...
We study zeta functions enumerating finite-dimensional irreducible complex linear representationsof ...
AbstractA theorem of Tate and Turner says that global function fields have the same zeta function if...
A theorem of Tate and Turner says that global function fields have the same zeta function if and onl...