Section: New Results

Computing solutions of linear Mahler equations

Mahler equations relate evaluations of the same function $f$ at iterated $b$th powers of the variable. They arise in particular in the study of automatic sequences and in the complexity analysis of divide-and-conquer algorithms. Recently, the problem of solving Mahler equations in closed form has occurred in connection with number-theoretic questions. A difficulty in the manipulation of Mahler equations is the exponential blow-up of degrees when applying a Mahler operator to a polynomial. In [3], Frédéric Chyzak and Philippe Dumas, together with Thomas Dreyfus (IRMA, Université de Strasbourg) and Marc Mezzarobba (external collaborator from Sorbonne Université), have presented algorithms for solving linear Mahler equations for series, polynomials, and rational functions, and have obtained polynomial-time complexity under a mild assumption. The article was formally accepted and published this year.