Wavelet analysis as a p–adic harmonic 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 is considered. This map (for p = 2) provides an equivalence between the constructed basis of eigenfunctions of the Vladimirov operator and the wavelet basis in L 2 (R) generated fro...

In this article, we generalize a result of Murty on the non-vanishing of complementary Bell numbers and irrationality of a p-adic series. This generalization leads to a sequence of polynomials. We partially answer the question of existence of an integral zero of those polynomials.

The ideals of the ring Zp are {0} and pZp, n ≥ 0. From this it follows that Zp is a discrete valuation ring, a principal ideal domain with exactly one maximal ideal, namely pZp; Zp is the valuation ring of Qp with the valuation vp. For n ≥ 1, Zp/pZp is isomorphic as a ring with Z/pZ. |x|p = p−vp(x), dp(x, y) = |x− y|p. With the topology induced by the metric dp, Qp is a locally compact abelian ...

In this work we explore the p-adic valuation of Eulerian numbers. We construct a tree whose nodes contain information about the p-adic valuation of these numbers. Using this tree, and some classical results for Bernoulli numbers, we compute the exact p divisibility for the Eulerian numbers when the first variable lies in a congruence class and p satisfies some regularity properties.