We prove that for p-optimal fields (a very large subclass of p-minimal fields containing all the known examples) a cell decomposition theorem follows from methods going back to Denef’s paper [Den84]. We derive from it the existence of definable Skolem functions and strong p-minimality, thus providing a new proof of the main result of [vdDHM99]. Then we turn to strongly p-optimal field satisfyin...

If R is a Dedekind domain, P a prime ideal of R and S ⊆R a finite subset then a P -ordering of S, as introduced by M. Bhargava in (J. Reine Angew. Math. 490:101–127, 1997), is an ordering {ai}i=1 of the elements of S with the property that, for each 1 < i ≤m, the choice of ai minimizes the P -adic valuation of ∏j<i(s− aj ) over elements s ∈ S. If S, S′ are two finite subsets of R of the same ca...

Wavelet analysis as a p–adic spectral analysis Abstract New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers (p–adic change of variable) is considered. p–Adic change of variable maps the Haar measure on p–adic numbers onto the Lebesgue measure on the positive semiline. p–Adic change of var...

Let $G$ be a reductive $p$-adic group‎. ‎We consider the general question‎ ‎of whether the reducibility of an induced representation can be detected in a‎ ‎``co-rank one‎" ‎situation‎. ‎For smooth complex representations induced from supercuspidal‎ ‎representations‎, ‎we show that a sufficient condition is the existence of a subquotient‎ ‎that does not appear as a subrepresentation‎. ‎An import...