Quasi-symmetric functions and mod p multiple harmonic sums

Details Quasi-symmetric functions and mod p multiple harmonic sums Quasi-symmetric functions and mod p multiple harmonic sums

2004-01-23

arxiv.org/abs/math/0401319v2

Mathematics

Number Theory

25 pages; revision updates cross-references and fixes typo in Theorem 7.5

Scientific paper

We present a number of results about (finite) multiple harmonic sums modulo a prime, which provide interesting parallels to known results about multiple zeta values (i.e., infinite multiple harmonic series). In particular, we prove a "duality" result for mod p multiple harmonic sums similar to (but distinct from) that for multiple zeta values. We also exploit the Hopf algebra structure of the quasi-symmetric functions to do calculations with multiple harmonic sums mod p, and obtain, for each weight n <= 9, a set of generators for the space of weight-n multiple harmonic sums mod p.

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