Applications of differential algebra to algebraic independence of arithmetic functions

DOI10.4064/AA8112-12-2015zbMath1347.11056arXiv1504.03263OpenAlexW1777083148MaRDI QIDQ2787079

Wai Yan Pong

Publication date: 24 February 2016

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03263

zbMATH Keywords

arithmetic functionsformal Dirichlet seriesalgebraic and linear independenceAx's theoremdifferential Schanuel conjecture

Mathematics Subject Classification ID

Algebraic independence; Gel'fond's method (11J85) Transcendence theory of other special functions (11J91) Arithmetic functions; related numbers; inversion formulas (11A25) Differential algebra (12H05) Irrationality; linear independence over a field (11J72)

Cites Work

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• The ring of number-theoretic functions
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• ÜBER DIRICHLETSCHE REIHEN UND HOLOMORPHE DIFFERENTIALGLEICHUNGEN
• Independence measures of arithmetic functions II
• On algebraic independence of dirichlet series
• On the convolution ring of arithmetic functions
• OBSERVATIONS ABOUT ALGEBRAIC DEPENDENCE OF DIRICHLET SERIES
• Colloquium De Giorgi 2013 and 2014

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