A p-ADIC VIEW OF MULTIPLE SUMS OF POWERS

Abstract

Washington [p-Adic L-functions and sums of powers, J. Number Theory69 (1998) 50–61] gave an explicit p-adic expansion of [Formula: see text] as a power series in m. The coefficients are values of p-adic L-functions. Let q = 4 if p = 2 and q = p otherwise. In this paper, we prove an explicit p-adic expansion of the multiple sums of powers [Formula: see text] as a p-adic power series in m. The coefficients are values of multiple two-variable p-adic L-functions. Washington's formula is a special case of the formula given in this paper when n = 1 and t = 0.