Arithmetic theory of q-difference equations (G_q-functions and\n q-difference modules of type G, global q-Gevrey series)

2009/02/24 by Lucia Di Vizio, Di Vizio, Lucia
Mathematics · Physics and Astronomy · #11J72 #12H99 #33D15 #39A13 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.0902.4169

openalex publication_date 2009/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the first part of the paper we give a definition of G_q-function and we\nestablish a regularity result, obtained as a combination of a q-analogue of the\nAndre'-Chudnovsky Theorem [And89, VI] and Katz Theorem [Kat70, S 13].\n In the second part of the paper, we combine it with some formal q-analogous\nFourier transformations, obtaining a statement on the irrationality of special\nvalues of the formal q-Borel transformation of a G_q-function.\n

Citations

• Cyclotomy and analytic geometry over F₁

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