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 -