1 citations · 1 across the 7 of their papers we have counts for
7 papers
On a family of continued fractions in associated to infinite binary words derived from the Thue-Morse sequence
Bill Allombert, Alain Lasjaunias
For each integer n > 1, we present an element in , having a power series expansion based on an infinite word W(n), over the alphabet ${+1;-1}g and whose continued fracti…
Unimodular Hunting II
Bill Allombert, Gaëtan Chenevier
Pursuing ideas in a recent work of the second author, we determine the isometry classes of unimodular lattices of rank 28, as well as the isometry classes of unimodular lattices of…
Group theory of cyclic cubic number fields
Daniel C. Mayer, Siham Aouissi, Bill Allombert +1
Astonishing new discoveries with quartets and octets of cyclic cubic fields sharing a common conductor are presented. Four kinds of graphs describing cubic residue conditions among…
Cyclic cubic number fields with harmonically balanced capitulation
Bill Allombert, Daniel C. Mayer
It is proved that c = 689347 = 31*37*601 is the smallest conductor of a cyclic cubic number field K whose maximal unramified pro-3-extension E = F(3,infinity,K) possesses an automo…
Symbolic Integration in Prime Characteristic
Bill Allombert
In this paper we study elementary extensions of differential fields in prime characteristic. In particular, we show that, in contrast to Liouville's result in characteristic zero,…
On a two-valued sequence and related continued fractions in power series fields
Bill Allombert, Nicolas Brisebarre, Alain Lasjaunias
We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. This continued fraction is a gen…
CM-Points on Straight Lines
Bill Allombert, Yuri Bilu, Amalia Pizarro-Madariaga
We prove that, with "obvious" exceptions, a CM-point (j(τ),j(τ')) cannot belong to a straight line in C^2 defined over Q. This generalizes a result of Kühne, who proved this for th…