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LINEAR INDEPENDENCE OF VALUES OF THE q-EXPONENTIAL AND RELATED FUNCTIONS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  23 October 2023

ANUP B. DIXIT Open the ORCID record for ANUP B. DIXIT [Opens in a new window] ,
VEEKESH KUMAR Open the ORCID record for VEEKESH KUMAR [Opens in a new window]  and
SIDDHI S. PATHAK Open the ORCID record for SIDDHI S. PATHAK [Opens in a new window]
ANUP B. DIXIT
Affiliation:
Institute of Mathematical Sciences (HBNI), CIT Campus Taramani, Chennai, Tamil Nadu 600113, India e-mail: anupdixit@imsc.res.in
VEEKESH KUMAR*
Affiliation:
Department of Mathematics, Indian Institute of Technology, Dharwad, Karnataka 580011, India
SIDDHI S. PATHAK
Affiliation:
Chennai Mathematical Institute, H-1 SIPCOT IT Park, Siruseri, Kelambakkam, Tamil Nadu 603103, India e-mail: siddhi@cmi.ac.in
*
e-mail: veekeshk@iitdh.ac.in
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Abstract

We establish the linear independence of values of the q-analogue of the exponential function and its derivatives at specified algebraic arguments, when q is a Pisot–Vijayaraghavan number. We also deduce similar results for cognate functions, such as the Tschakaloff function and certain generalised q-series.

Keywords

q-exponential functionq-logarithm functionPV number

MSC classification

Primary: 11J72: Irrationality; linear independence over a field

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 3 , June 2024 , pp. 453 - 463
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Research of the first and the third authors was partially supported by the INSPIRE Faculty Fellowship.

References

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