相关论文: Hodge integrals, Hurwitz numbers, and Symmetric Gr…
We find the Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which is very close to certain mock theta functions. We also prove two combinatorial interpretation of Hurwitz class numbers appeared…
We consider graded Cartan matrices of the symmetric groups and the Iwahori-Hecke algebras of type A, which have entries in the ring $\mathbb Z[v,v^{-1}]$. These matrices may also be interpreted as Gram matrices of the Shapovalov form on…
In terms of the derivative operator and three hypergeometric series identities, several interesting summation formulas involving generalized harmonic numbers are established.
We prove sum formulas for double polylogarithms of Hurwitz type, that is, involving a shifting parameter $b$ in the denominator. These formulas especially imply well-known sum formulas for double zeta values, and sum formulas for double…
We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa-Kaneko zeta function, complementing and generalizing earlier…
We are extending results from \cite{B-Hurwitz} by building a parallel theory of simple Hurwitz numbers for the reflection groups $G(m,1,n)$. We also study analogs of the cut-and-join operators. An algebraic description as well as a…
We present a method for calculating any (nested) harmonic sum to arbitrary accuracy for all complex values of the argument. The method utilizes the relation between harmonic sums and (derivatives of) Hurwitz zeta functions, which allows a…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
The basis elements spanning the Sato Grassmannian element corresponding to the KP $\tau$-function that serves as generating function for rationally weighted Hurwitz numbers are shown to be Meijer $G$-functions. Using their Mellin-Barnes…
Given $b=-A\pm i$ with $A$ being a positive integer, we can represent any complex number as a power series in $b$ with coefficients in $\mathcal A=\{0,1,\ldots, A^2\}$. We prove that, for any real $\tau\geq 2$ and any non-empty proper…
We determine the structure of the Hodge ring, a natural object encoding the Hodge numbers of all compact Kaehler manifolds. As a consequence of this structure, there are no unexpected relations among the Hodge numbers, and no essential…
We show that integrals involving log-tangent function, with respect to certain square-integrable functions on $(0, \pi/2)$, can be evaluated by some series involving the harmonic number. Then we use this result to establish many closed…
We study the Hodge numbers of Landau-Ginzburg models as defined by Katzarkov, Kontsevich and Pantev. First we show that these numbers can be computed using ordinary mixed Hodge theory, then we give a concrete recipe for computing these…
We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.
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…
We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inverses of $2\times 2$ block operator matrices. These…
We consider some closed-form evaluations of certain infinite sums involving the Hurwitz zeta function $\zeta(s,\alpha)$ of the form \[\sum_{k=1}^\infty (\pm 1)^k k^m \zeta(s,k),\] where $m$ is a non-negative integer. For the sums with $m=0$…
Motivated by the orthogonality relations for irreducible characters of a finite group, we evaluate the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements. We then discuss results for…
Nahm sums are specific $q$-hypergeometric series associated with symmetric positive definite matrices. In this paper we study Nahm sums associated with symmetrizable matrices. We show that one direction of Nahm's conjecture, which was…
During 2022--2023 Z.-W. Sun posed many conjectures on infinite series with summands involving generalized harmonic numbers. Motivated by this, we deduce $58$ series identities involving harmonic numbers, eight of which were previously…