Constant term evaluation and two kinds of congruence

Abstract

We consider two kinds of congruence proposed recently by Sun. The first one is of the form [Formula: see text], where [Formula: see text] is a prime, [Formula: see text] is a character and [Formula: see text] is a sequence of integers. By using a constant term expression for [Formula: see text], we derive congruence for two sequences [Formula: see text]. The second one involves the sum [Formula: see text] where [Formula: see text] By giving a constant term expression for [Formula: see text], we derive a congruence for [Formula: see text] modulo a prime [Formula: see text].