Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions

DOI10.1142/S1793042122500099zbMath1498.11163arXiv2008.07136MaRDI QIDQ5025441

Andreas Maurischat, Rudolph Bronson Perkins

Publication date: 2 February 2022

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.07136

zbMATH Keywords

Drinfeld modulesGalois representationsTaylor coefficientsAnderson generating functionshyperderivatives

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Galois representations (11F80) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Transcendence theory of Drinfel'd and (t)-modules (11J93) Special functions in characteristic (p) (gamma functions, etc.) (33E50) Ordinary differential operators (34L99)

Cites Work

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• Values of certain \(L\)-series in positive characteristic
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• On Drinfeld modular forms of higher rank IV: modular forms with level
• Periods of \(t\)-modules as special values
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• Universal Gauss-Thakur sums and \(L\)-series
• Identities for Anderson generating functions for Drinfeld modules
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• A difference version of Nori's theorem
• A categorical approach to Picard-Vessiot theory
• Algebraic independence of periods and logarithms of Drinfeld modules
• Vectorial Drinfeld modular forms over Tate algebras
• An Integral Digit Derivative Basis for Carlitz Prime Power Torsion Extensions

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