Bill Allombert
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View article: On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence
On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence Open
For each integer n > 1, we present an element in $Q((T^-1))$, having a power series expansion based on an infinite word W(n), over the alphabet ${+1;-1}g and whose continued fraction expansion has a particular pattern which is explicitly d…
View article: Unimodular Hunting II
Unimodular Hunting II Open
Pursuing ideas in [6], we determine the isometry classes of unimodular lattices of rank $28$ , as well as the isometry classes of unimodular lattices of rank $29$ without nonzero vectors of norm $\leq 2$ . We also provide some invariant th…
View article: PEARL-SCALLOP: Parameter Extension Applicable in Real Life for SCALLOP
PEARL-SCALLOP: Parameter Extension Applicable in Real Life for SCALLOP Open
A crucial ingredient for many cryptographic primitives such as key exchange protocols and advanced signature schemes is a commutative group action where the structure of the underlying group can be computed efficiently. SCALLOP provides su…
View article: Unimodular Hunting II
Unimodular Hunting II Open
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 rank 29 without nonzero vectors of norm <=2.
View article: Group theory of cyclic cubic number fields
Group theory of cyclic cubic number fields Open
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 the prime divisors of the conductor enforce elementary bi-…
View article: Cyclic cubic number fields with harmonically balanced capitulation
Cyclic cubic number fields with harmonically balanced capitulation Open
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 automorphism group G = Gal(E/K) of order 6561 with coinciding rel…
View article: Bill Allombert - Start of Atelier (setting up personal computers)
Bill Allombert - Start of Atelier (setting up personal computers) Open
This talk focuses on the current development version of the PARI library (2.12.*), available from our GIT repository, see http://pari.math.u-bordeaux.fr/anongit.html
The text of this talk is available in the files sources.* in http://pari…
View article: Symbolic Integration in Prime Characteristic
Symbolic Integration in Prime Characteristic Open
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, all elements of an elementary extension admit an antideriva…
View article: On a two-valued sequence and related continued fractions in power series fields
On a two-valued sequence and related continued fractions in power series fields Open
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 generating function of a particular sequence in the set {1, 2}…
View article: From a quartic continued fraction in $\mathbb{F}_3((T^-1))$ to a transcendental continued fraction in $\mathbb{Q}((T^-1))$ through an infinite word over {1,2}
From a quartic continued fraction in $\mathbb{F}_3((T^-1))$ to a transcendental continued fraction in $\mathbb{Q}((T^-1))$ through an infinite word over {1,2} Open
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 generating function of a particular sequence in the set {1, 2}…
View article: Euler's divergent series and an elementary model in statistical physics
Euler's divergent series and an elementary model in statistical physics Open
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