An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials

2004/06/30 by Boris Y. Rubinstein, Rubinstein, Boris Y.
Mathematics · #11P81 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11P81

paper · pdf · doi:10.48550/arxiv.math/0407001

8 pages, submitted to The Ramanujan Journal

arxiv created 2004/06/30 · arxiv updated 2009/12/01

Abstract

Explicit expressions for restricted partition function W(s,\bf d^m) and its quasiperiodic components W_j(s,\bf d^m) (called Sylvester waves) for a set of positive integers \bf d^m = \d₁, d₂, ..., d_m\ are derived. The formulas are represented in a form of a finite sum over Bernoulli polynomials of higher order with periodic coefficients.

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