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We prove the rationality of the Łojasiewicz exponent for p-adic semi-algebraic functions without compactness hypothesis. In the parametric case, we show that the parameter space can be divided into a finite number of semi-algebraic sets on each of which the Łojasiewicz exponent is constant.

Familles normales de fractions rationnelles et ensembles fermés de nombres algébriques

Charles Pisot (1962/1963)

Séminaire Dubreil. Algèbre et théorie des nombres

Haar wavelets on the Lebesgue spaces of local fields of positive characteristic

Biswaranjan Behera (2014)

Colloquium Mathematicae

We construct the Haar wavelets on a local field K of positive characteristic and show that the Haar wavelet system forms an unconditional basis for $L^{p} (K)$ , 1 < p < ∞. We also prove that this system, normalized in $L^{p} (K)$ , is a democratic basis of $L^{p} (K)$ . This also proves that the Haar system is a greedy basis of $L^{p} (K)$ for 1 < p < ∞.

Kloosterman sums for prime powers in P-adic fields

Stanley J. Gurak (2009)

Journal de Théorie des Nombres de Bordeaux

Let $K$ be a field of degree $n$ over $Q_{p}$ , the field of rational $p$ -adic numbers, say with residue degree $f$ , ramification index $e$ and differential exponent $d$ . Let $O$ be the ring of integers of $K$ and $P$ its unique prime ideal. The trace and norm maps for $K / Q_{p}$ are denoted $T r$ and $N$ , respectively. Fix $q = p^{r}$ , a power of a prime $p$ , and let $η$ be a numerical character defined modulo $q$ and of order $o (η)$ . The character $η$ extends to the ring of $p$ -adic integers $ℤ_{p}$ in the natural way; namely $η (u) = η (\tilde{u})$ , where $\tilde{u}$ denotes the residue class...

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A weak Néron model with applications to $p$ -adic dynamical systems

Algebraic Weyl system and application

An explicit 2nth reciprocity law.

Automata and the arithmetic of formal power series

Barnes' identities and representations of GL (2). II. Nonarchimedian local field case.

Chains of metric invariants over a local field

Ein v. Staudt-Clausenscher Satz für periodische Bernoullizahlen.

Elementary equivalence and codimension in p-adic fields.

Exposants de Lojasiewicz dans le cas semi-algebrique p-adique

Familles normales de fractions rationnelles et ensembles fermés de nombres algébriques

Haar wavelets on the Lebesgue spaces of local fields of positive characteristic

Kloosterman sums for prime powers in P-adic fields

Limit theorems for uniformly distributed p-adic sequences

Mesures p-adiques et éléments analytiques.

Normal bases of rings of continuous functions constructed with the (qₙ)-digit principle

Note on $q$ -Nasybullin's lemma associated with the modified $p$ -adic $q$ -Euler measure.

p-adic Dedekind sums.

Periodicity of p-adic continued fractions.

Periodizitätseigenschaften p-adischer Kettenbrüche.

Pour l'étude des groupes de ramification

Currently displaying 1 – 20 of 27