TY  - JOUR
ID  - Ogawara2017
LB  - Ogawara2017
AU  - Ogawara, Hiroshi
TI  - On criteria for algebraic independence of collections of functions satisfying algebraic difference relations
ST  - On criteria for algebraic independence of collections of functions satisfying algebraic difference relations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 3
SP  - 457
EP  - 472
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.3.457
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.3.457
AB  - This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1) Vignéras' multiple gamma functions and derivatives of the gamma function, (2) the logarithmic function, \(q\)-exponential functions and \(q\)-polylogarithm functions. In a similar way, we give a generalization of Ostrowski's theorem.
KW  - difference algebra
KW  - systems of algebraic difference equations
KW  - algebraic independence
KW  - Vignéras' multiple gamma functions
KW  - \(q\)-polylogarithm functions
SN  - 1232-9274
ER  -