Multiple series connected to Hoffman's conjecture on multiple zeta values

Details Multiple series connected to Hoffman's conjecture on multiple zeta values Multiple series connected to Hoffman's conjecture on multiple zeta values

2006-09-28

arxiv.org/abs/math/0609799v2

Journal of Algebra 320 (2008), 1682-1703

Mathematics

Number Theory

26 pages; small modifications

Scientific paper

Recent results of Zlobin and Cresson-Fischler-Rivoal allow one to decompose any suitable $p$-uple series of hypergeometric type into a linear combination (over the rationals) of multiple zeta values of depth at most $p$; in some cases, only the multiple zeta values with 2's and 3's are involved (as in Hoffman's conjecture). In this text, we study the depth $p$ part of this linear combination, namely the contribution of the multiple zeta values of depth exactly $p$. We prove that it satisfies some symmetry property as soon as the $p$-uple series does, and make some conjectures on the depth $p-1$ part of the linear combination when $p=3$. Our result generalizes the property that (very) well-poised univariate hypergeometric series involve only zeta values of a given parity, which is crucial in the proof by Rivoal and Ball-Rivoal that $\zeta(2n+1)$ is irrational for infinitely many $n \geq 1$.

Affiliated with

Also associated with

No associations

Rating

Multiple series connected to Hoffman's conjecture on multiple zeta values does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multiple series connected to Hoffman's conjecture on multiple zeta values, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multiple series connected to Hoffman's conjecture on multiple zeta values will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-532305