We analyze Chiodo’s formulas for the Chern classes related to the r -th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with ψ-classes are reproduced via the Chekhov–Eynard–Orantin topological recursion. As an application, we prove that the Johnson-Pandharipande-Tseng formula for the orbifold Hurwitz nu...

We study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch points. Generalizing the phenomenon observed for double Hurwitz numbers, such cycles are piecewise polynomial in the entries of the special ramification; the chambers of polynomiality and wall crossings have an expli...

A number of authors have considered mean values of powers of the modulus of the Hurwitz zeta function ζ(s, a), see [3, 4, 5, 6, 7]. In this paper, the mean of the function itself is considered. First a functional equation relating the Riemann zeta function to sums of the values of the Hurwitz zeta function at rational values of a is derived. This functional equation underlies the vanishing of t...

This paper studies the analogue of Hurwitz groups and surfaces in the context of harmonic group actions on finite graphs. Our main result states that maximal graph groups are exactly the finite quotients of the modular group Γ = 〈 x, y | x2 = y3 = 1 〉 of size at least 6. As an immediate consequence, every Hurwitz group is a maximal graph group, and the final section of the paper establishes a d...

The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.

This note presents an elementary proof of the familiar Routh-Hurwitz test. The proof is basically one continuity argument, it does not rely on Sturm chains, Cauchy index and the principle of the argument and it is fully self-contained. In the same style an extended Routh-Hurwitz test is derived, which finds the inertia of polynomials.

Based on an inversion of the Routh table construction, a unimodular characterization of all Hurwitz polynomials is obtained. In parameter space, the Hurwitz polynomials of degree n correspond to the positive 2-tant. The method is then used to construct classes of stable continuous-time delay-difference equations and delay differential equations of neutral type, by a suitable limiting process.