TY - JOUR
T1 - Transformations of well-poised hypergeometric functions over finite fields
AU - McCarthy, Dermot
PY - 2012/11
Y1 - 2012/11
N2 - We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are analogous to those given by Dixon, Kummer and Whipple for the well-poised classical series. We also discuss this functionʼs relationship to other finite field analogues of the classical series, most notably those defined by Greene and Katz.
AB - We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are analogous to those given by Dixon, Kummer and Whipple for the well-poised classical series. We also discuss this functionʼs relationship to other finite field analogues of the classical series, most notably those defined by Greene and Katz.
U2 - 10.1016/j.ffa.2012.08.007
DO - 10.1016/j.ffa.2012.08.007
M3 - Article
SP - 1133
EP - 1147
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
ER -