14,526 research outputs found
Duality for Finite Multiple Harmonic q-Series
We define two finite q-analogs of certain multiple harmonic series with an
arbitrary number of free parameters, and prove identities for these q-analogs,
expressing them in terms of multiply nested sums involving the Gaussian
binomial coefficients. Special cases of these identities--for example, with all
parameters equal to 1--have occurred in the literature. The special case with
only one parameter reduces to an identity for the divisor generating function,
which has received some attention in connection with problems in sorting
theory. The general case can be viewed as a duality result, reminiscent of the
duality relation for the ordinary multiple zeta function.Comment: 12 pages AMSLaTeX. Submitted for publication October 26, 2003;
revised September 14, 2004. New title reflects change in emphasis and new
section devoted to connections with inverse pairs and Hoffman duality.
References added and typos correcte
Cyclotomic analogues of finite multiple zeta values
We introduce the notion of finite multiple harmonic q-series at a primitive
root of unity and show that these specialize to the finite multiple zeta value
(FMZV) and the symmetrized multiple zeta value (SMZV) through an algebraic and
analytic operation, respectively. Further, we obtain families of linear
relations among these series which induce linear relations among FMZVs and
SMZVs of the same form. This gives evidence towards a conjecture of Kaneko and
Zagier relating FMZVs and SMZVs. Motivated by the above results, we define
cyclotomic analogues of FMZVs, which conjecturally generate a vector space of
the same dimension as that spanned by the finite multiple harmonic q-series at
a primitive root of unity of sufficiently large degree.Comment: 23 page
A class of relations among multiple zeta values
We prove a new class of relations among multiple zeta values (MZV's) which
contains Ohno's relation. We also give the formula for the maximal number of
independent MZV's of fixed weight, under our new relations. To derive our
formula for MZV's we consider the Newton series whose values at non-negative
integers are finite multiple harmonic sums.Comment: 36 pages, presentation improved, to appear in Journal of Number
Theor
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