Abstract
G-functions appeared in Siegel’s paper [56] about diophan-tine approximation, and led in this context to an extensive literature (see [7] for a small list). In this chapter we present a definition of G-functions (inspired by Bombieri “local-to-global” setting [7]), and define two basic related invariants, namely the size Σ (which coincides with Bombieri’s one, ibid.) and the global radius. We then turn to examples: rational functions, diagonals, polylogarithms and generalized hypergeometric functions, which we study with some detail; our presentation of diagonals is inspired by Christol [14]. At last we gather some “pathologies”.
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© 1989 Springer Fachmedien Wiesbaden
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André, Y. (1989). G-Functions. In: G-Functions and Geometry. Aspects of Mathematics / Aspekte der Mathematik, vol E 13. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14108-2_2
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DOI: https://doi.org/10.1007/978-3-663-14108-2_2
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-06317-7
Online ISBN: 978-3-663-14108-2
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