A density theorem for the difference Galois groups of regular singular Mahler equations

Marina Poulet (1, 2)

1 UCBL - Université Claude Bernard Lyon 1
2 CTN - Combinatoire, théorie des nombres

The difference Galois theory of Mahler equations is an active research area. The present paper aims at developing the analytic aspects of this theory. We first attach a pair of connection matrices to any regular singular Mahler equation. We then show that these connection matrices can be used to produce a Zariski-dense subgroup of the difference Galois group of any regular singular Mahler equation.

Mots clés: Mahler equations; difference Galois theory; density theorem

Domaines: Mathématiques générales [math.GM]

Marina Poulet. A density theorem for the difference Galois groups of regular singular Mahler equations. International Mathematics Research Notices, 2021, ⟨10.1093/imrn/rnab277⟩. ⟨hal-03084197v2⟩