2011/03/25 by Lucia Di Vizio, DI Vizio, Lucia, Charlotte Hardouin +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #12H99 #39A13 #39A99 #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Polynomial and algebraic computation #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1103.5067
openalex publication_date 2011/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper essentially contains two results that generalize and improve some of the constructions of [arXiv:0801.1493]. First of all, in the case of one derivation, we prove that the parameterized Galois theory for difference equations constructed in [arXiv:0801.1493] can be descended from a differentially closed to an algebraically closed field. In the second part of the paper, we show that the theory can be applied to deformations of q-series, to study the differential dependency with respect to x(d)/(dx) and q(d)/(dq). We show that the parameterized difference Galois group (with respect to a convenient derivation defined in the text) of the Jacobi Theta function can be considered as the Galoisian counterpart of the heat equation.