6 citations · 14 across the 12 of their papers we have counts for
5 papers · 1 filter
Grothendieck rings of \mathbb{Z}-valued fields
Raf Cluckers, Deirdre Haskell
We prove the triviality of the Grothendieck ring of a integer-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the p…
Classification of semi-algebraic -adic sets up to semi-algebraic bijection
Raf Cluckers
We prove that two infinite p-adic semi-algebraic sets are isomorphic (i.e. there exists a semi-algebraic bijection between them) if and only if they have the same dimension.
Model theory of valued fields
Raf Cluckers
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.
Multivariate Igusa theory: Decay rates of exponential sums
Raf Cluckers
We obtain general estimates for exponential integrals of the form \[ E_f(y)=\int_{\mathbb{Z}_{p}^{n}}ψ(\sum_{j=1}^r y_j f_j(x))|dx|, \] where the are restricted power series…
Cell decomposition and p-adic integration
Raf Cluckers
A semialgebraic bijection from the field of p-adic numbers to itself minus one point is constructed. Semialgebraic p-adic sets are classified up to semialgebraic bijection. A cell…