In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to p-adic number fields. As an application , we show how strings over a finite alphabet can be encoded in cyclotomic extensions of Qp and discuss p-adic DNA encoding. The application leads to fast p-adic agglomerative hierarchic algorithms similar to the ones recently used e....

We study the p-adic behavior of Jacobi sums for Q(ζp) and link this study to the p-Sylow subgroup of the class group of Q(ζp) + and to some properties of the jacobian of the Fermat curve Xp + Y p = 1 over Fl where l is a prime number distinct from p. Let p be a prime number, p ≥ 5. Iwasawa has shown that the p-adic properties of Jacobi sums for Q(ζp) are linked to Vandiver’s Conjecture (see [5]...

For ψ a nontrivial additive character on the finite field Fq, observe that the map t 7→ P x∈Fq ψ(f(x) + tx) is the Fourier transform of the map t 7→ ψ(f(t)). As is well-known, this has a cohomological interpretation, producing a continuous l-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both l-adic and p-adic meth...

An effective p-adic encoding of dendrograms is presented through an explicit embedding into the Bruhat-Tits tree for a p-adic number field. This field depends on the number of children of a vertex and is a finite extension of the field of p-adic numbers. It is shown that fixing p-adic representatives of the residue field allows a natural way of encoding strings by identifying a given alphabet w...

References [1] S. Akiyama, T. Borbéli, H. Brunotte, A. Pethö, and J. Thuswaldner. Generalized radix representations and dynamical systems i. Acta Math. Hungarica., 108:207–238, 2005. [2] S. Akiyama, H. Brunotte, A. Pethö, and J. Thuswaldner. Generalized radix representations and dynamical systems ii. Acta Arith., 121:21–61, 2006. [3] S. Akiyama and N Gjini. On the connectedness of self-affine a...

To Dong-Sik Kim on his 62nd birthday We try to generalize an explicit construction for an orthonormal system of eigen-functions of the Vladimirov operator on L 2 (Q n p) which was originally given by Vladimirov (1988). Also the multiwavelet analysis can be considered as the p-adic spectral analysis in L 2 (Q n p), using in part the recent work of Kozyrev (2002). denote the ring of integers, the...

Rigged Hilbert space of the free coherent states is investigated. We prove that this rigged Hilbert space is isomorphous to the space of generalized functions over p–adic disk. We discuss the relation of the described isomorphism of rigged Hilbert spaces and noncommutative geometry and show, that the considered example realises the isomorphism of the noncommutative line and p–adic disk. In the ...

We develop a mathematically-motivated algorithm for image superresolution, based on the discrete shearlet transform. The shearlet transform is strongly directional, and is known to provide nearoptimally sparse representations for a broad class of images. This often leads to superior performance in edge detection and image representation, when compared to other isotropic frames. We justify the u...