A generalization of multiple zeta values. Part 2: Multiple sums
- 18 April 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 28 (2), 200-233
- https://doi.org/10.7546/nntdm.2022.28.2.200-233
Abstract
Multiple zeta values have become of great interest due to their numerous applications in mathematics and physics. In this article, we present a generalization, which we will refer to as multiple sums, where the reciprocals are replaced with arbitrary sequences. We develop formulae to help with manipulating such sums. We develop variation formulae that express the variation of multiple sums in terms of lower order multiple sums. Additionally, we derive a set of partition identities that we use to prove a reduction theorem that expresses multiple sums as a combination of simple sums. We present a variety of applications including applications concerning polynomials and MZVs such as generating functions and expressions for ((zeta 2p}(m)) and (zeta*({2p}(m)). Finally, we establish the connection between multiple sums and a type of sums called recurrent sums. By exploiting this connection, we provide additional partition identities for odd and even partitions.Keywords
This publication has 7 references indexed in Scilit:
- Partition zeta functionsResearch in Number Theory, 2016
- Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass formsAdvances in Mathematics, 2013
- Multiple Zeta Values and Modular Forms in Quantum Field TheoryTexts & Monographs in Symbolic Computation, 2013
- On generating functions of multiple zeta values and generalized hypergeometric functionsmanuscripta mathematica, 2010
- The Multiple Zeta Value data mineComputer Physics Communications, 2010
- Harmonic sums and Mellin transforms up to two-loop orderPhysical Review D, 1999
- Some variants of Ferrers diagramsJournal of Combinatorial Theory, Series A, 1989