50 citations · 72 across the 6 of their papers we have counts for
7 papers
Fast Coefficient Computation for Algebraic Power Series in Positive Characteristic
Alin Bostan, Xavier Caruso, Gilles Christol +1
We revisit Christol's theorem on algebraic power series in positive characteristic and propose yet another proof for it. This new proof combines several ingredients and advantages…
Becker's conjecture on Mahler functions
Jason Bell, Frederic Chyzak, Michael Coons +1
In 1994, Becker conjectured that if is a -regular power series, then there exists a -regular rational function such that satisfies a Mahler-type fun…
Computing solutions of linear Mahler equations
Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas +1
Mahler equations relate evaluations of the same function at iterated th powers of the variable. They arise in particular in the study of automatic sequences and in the compl…
Fast Computation of the Nth Term of an Algebraic Series over a Finite Prime Field
Alin Bostan, Gilles Christol, Philippe Dumas
We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the th coefficient…
Rational series and asymptotic expansion for linear homogeneous divide-and-conquer recurrences
Philippe Dumas
Among all sequences that satisfy a divide-and-conquer recurrence, the sequences that are rational with respect to a numeration system are certainly the most immediate and most esse…
Wronskians and linear independence
Alin Bostan, Philippe Dumas
We give a new and simple proof of the fact that a finite family of analytic functions has a zero Wronskian only if it is linearly dependent.