REVIEW 3 cited by
Values and derivative values at nonpositive integers of generalized multiple Hurwitz zeta functions
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We establish the meromorphic continuation of certain multiple zeta functions of generalized Hurwitz type. From this meromorphic continuation, we obtain explicit formulas for their (derivative) values at nonpositive integers along a given direction. As an application, we provide explicit formulas for some values and derivative values of the Witten zeta functions $\zeta_{\mathfrak{g}_2}$ and $\zeta_{\mathfrak{so}(5)}$. Furthermore, by employing a Meinardus-type theorem, we investigate the asymptotic behavior of the number of $n$-dimensional representations of the exceptional Lie algebra $\mathfrak{g}_2$.
Forward citations
Cited by 3 Pith papers
-
Generic polar divisors and flag residues for root-system zeta functions
For every irreducible root system, the genuine polar divisors of the KMT zeta function are exactly the carrier hyperplanes, with explicit residue formulas.
-
Vanishing of Witten zeta function at negative integers
For every root system, the Witten zeta function vanishes to order at least the rank at negative even integers, and its leading coefficient is a Q-linear combination of Hurwitz zeta values.
-
Values at non-positive integers of partially twisted multiple zeta-functions II
For partially twisted multiple zeta-functions with polynomial denominators, the paper proves explicit formulas for the special values at non-positive integers and exhibits transcendental values in examples.
Discussion (0). Continue with ORCID to comment.