- 著者
- Michael E. HOFFMAN
- 出版者
- Faculty of Mathematics, Kyushu University
- 雑誌
- Kyushu Journal of Mathematics (ISSN:13406116)
- 巻号頁・発行日
- vol.69, no.2, pp.345-366, 2015 (Released:2015-10-13)
- 参考文献数
- 30
- 被引用文献数
- 19 41
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 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 perform calculations with multiple harmonic sums mod p, and obtain, for each weight n through nine, a set of generators for the space of weight-n multiple harmonic sums mod p. When combined with recent work, the results of this paper offer significant evidence that the number of quantities needed to generate the weight-n multiple harmonic sums mod p is the nth Padovan number (OEIS sequence A000931).