Algebraic independence of the Carlitz period and its hyperderivatives

DOI10.1016/J.JNT.2022.01.006zbMath1502.11082arXiv2104.02630OpenAlexW3147997544WikidataQ114156593 ScholiaQ114156593MaRDI QIDQ2161330

Andreas Maurischat

Publication date: 4 August 2022

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

Full work available at URL: https://arxiv.org/abs/2104.02630

zbMATH Keywords

transcendenceDrinfeld modulesperiodshigher derivationshyperdifferentialst-modules

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Transcendence theory of Drinfel'd and (t)-modules (11J93)

Cites Work

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• Tensor powers of the Carlitz module and zeta values
• A note on a refined version of Anderson-Brownawell-Papanikolas criterion
• Algebraic independence in characteristic two
• The digit principle
• Prolongations of \(t\)-motives and algebraic independence of periods
• Derivatives of a Drinfeld module and transcendence
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Certain quantities transcendental over \(\text{GF}(p^n,x)\)
• Linear independence and divided derivatives of a Drinfeld module II
• An Integral Digit Derivative Basis for Carlitz Prime Power Torsion Extensions

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