Linear independence of values of the $q$-exponential and related functions

Anup B. Dixit; Veekesh Kumar; Siddhi S. Pathak

Linear independence of values of the $q$-exponential and related functions

Number Theory 2023-09-01 v3

Authors: Anup B. Dixit , Veekesh Kumar , Siddhi S. Pathak

Abstract

In this paper, we establish the linear independence of values of the $q$ -analogue of the exponential function, $E_q(x)$ and its derivatives at specified algebraic arguments, when $q$ is a Pisot-Vijayraghavan number. We also deduce similar results for cognate functions, such as the Tschakaloff function and certain generalized $q$ -series.

Keywords

linear independence q-exponential function pisot-vijayraghavan number tschakaloff function q-series algebraic arguments

Cite

@article{arxiv.2211.03030,
  title  = {Linear independence of values of the $q$-exponential and related functions},
  author = {Anup B. Dixit and Veekesh Kumar and Siddhi S. Pathak},
  journal= {arXiv preprint arXiv:2211.03030},
  year   = {2023}
}

Comments

Bulletin of Australian Math. Soc., To appear

Linear independence of values of the $q$-exponential and related functions

Abstract

Keywords

Cite

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