Related papers: Some relations for one-part double Hurwitz numbers
Double Hurwitz numbers count branched covers of the projective line with fixed branch points, with simple branching required over all but two points 0 and infinity, and the branching over 0 and infinity specified by partitions of the degree…
In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.
We consider the problem of deducing the duality relation from the extended double shuffle relation for multiple zeta values. Especially we prove that the duality relation for double zeta values and that for the sum of multiple zeta values…
Hurwitz numbers with completed cycles are standard Hurwitz numbers with simple branch points replaced by completed cycles. In fact, simple branch points correspond to completed $2$-cycles. Okounkov and Pandharipande have established the…
In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.
Short introduction to the gauge/gravity duality
We consider some bases in the Hecke algebra and exhibit certain dualities between them.
In this paper, we give an optimal estimate of an average of Hurwitz class numbers. As an application, we give an equidistribution result of the family $\{\frac{t}{2q^{\nu/2}} \ | \ \nu \in \mathbb{N}, t \in \mathbb{Z}, |t|<2q^{\nu/2}\}$…
In this paper, we study a certain type of Hurwitz numbers which count branched covers over the Riemann sphere admitting several branch points with fixed ramification types, one branch point with a fixed number of preimages, and one branch…
We obtain another proof of Hermite's integral for the Hurwitz zeta function.
Hurwitz numbers count covers of curves satisfying fixed ramification data. Via monodromy representation, this counting problem can be transformed to a problem of counting factorizations in the symmetric group. This and other beautiful…
Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at…
The functional relation of the Hurwitz zeta function is proved by using the connection problem of the confluent hypergeometric equation.
This research paper focuses on exploring two Complex-valued function's fractional derivative, specifically the Hurwitz Zeta function and Jacobi theta function. The study is based on the Complex Generalization of Grunwald-Letnikov Fractional…
The asymptotic study of class numbers of binary quadratic forms is a foundational problem in arithmetic statistics. Here, we investigate finer statistics of class numbers by studying their self-correlations under additive shifts.…
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
By considering the intersections of Shimura curves and Humbert surfaces on the Siegel modular threefold, we obtain new class number relations. The result is a higher-dimensional analogue of the classical Hurwitz-Kronecker class number…
We first survey the known results on functional equations for the double zeta-function of Euler type and its various generalizations. Then we prove two new functional equations for double series of Euler-Hurwitz-Barnes type with complex…
We introduce and study a `level two' generalization of the poly-Bernoulli numbers, which may also be regarded as a generalization of the cosecant numbers. We prove a recurrence relation, two exact formulas, and a duality relation for…
In this paper, we study some properties of Whitney numbers of Dowling lattices and related polynomials. We answer the following question: there is relation between Stirling and Eulerian polynomials. Can we find a new relation between…