40 citations · 178 across the 39 of their papers we have counts for
8 papers · 1 filter
On the monoid generated by a Lucas sequence
Clemens Heuberger, Stephan Wagner
A Lucas sequence is a sequence of the general form , where and are real algebraic integers such that and are both ra…
Elliptic Curves with Isomorphic Groups of Points over Finite Field Extensions
Clemens Heuberger, Michela Mazzoli
Consider a pair of ordinary elliptic curves and defined over the same finite field . Suppose they have the same number of -rational points, i.e…
Canonical Trees, Compact Prefix-free Codes and Sums of Unit Fractions: A Probabilistic Analysis
Clemens Heuberger, Daniel Krenn, Stephan Wagner
For fixed , we consider the class of representations of as sum of unit fractions whose denominators are powers of or equivalently the class of canonical compact …
Analysis of the binary asymmetric joint sparse form
Clemens Heuberger, Sara Kropf
We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of nonzero digit vectors. This lea…
Existence and Optimality of -Non-adjacent Forms with an Algebraic Integer Base
Clemens Heuberger, Daniel Krenn
We consider digital expansions in lattices with endomorphisms acting as base. We focus on the -non-adjacent form (-NAF), where each block of consecutive digits contains a…
Optimality of the Width- Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases
Clemens Heuberger, Daniel Krenn
Efficient scalar multiplication in Abelian groups (which is an important operation in public key cryptography) can be performed using digital expansions. Apart from rational intege…
Analysis of Width- Non-Adjacent Forms to Imaginary Quadratic Bases
Clemens Heuberger, Daniel Krenn
We consider digital expansions to the base of , where is an algebraic integer. For a , the set of admissible digits consists of 0 and one representative of every r…
A precise description of the p-adic valuation of the number of alternating sign matrices
Clemens Heuberger, Helmut Prodinger
Following Sun and Moll, we study v_p(T(N)), the p-adic valuation of the counting function of the alternating sign matrices. We find an exact analytic expression for it that exhibit…