A p-ADIC VIEW OF MULTIPLE SUMS OF POWERS

作者：Kim Min Soo; Hu Su

来源：International Journal of Number Theory, 2011, 7(8): 2273-2288.

DOI：10.1142/S1793042111005027

• Higher-order Bernoulli polynomials
• multiple Bernoulli'
• s formula
• multiple two-variable p-adic L-functions
• multiple sums of powers

Washington [p-Adic L-functions and sums of powers, J. Number Theory 69 (1998) 50-61] gave an explicit p-adic expansion of
Sigma(mp)(j=1p(sic)) 1/j(r)
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
Sigma(j1, ..., jn= 0) (mp-1)(p(sic)(j1+ ... +jn)) 1/(qt + j1 + ... + jn) (r+ n-1)
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.

• 出版日期2011-12