Let f : Σ̃ d:1 −→ Π Σ denote a branched cover between closed, connected, and orientable surfaces, where d is the global degree, Π = {Π1, . . . ,Πn}, n is the number of branching points, and Πi is the partition of d given by the local degrees over the i-th branching point. If l(Π) is the total length of Π, then the Riemmann-Hurwitz formula asserts that χ(Σ̃) − l(Π) = d · (χ(Σ) − n). A candidate br...

We define maps which induce mediant convergents of Rosen continued fractions and discuss arithmetic and metric properties of mediant convergents. In particular, we show equality of the ergodic theoretic Lenstra constant with the arithmetic Legendre constant for each of these maps. This value is sufficiently small that the mediant Rosen convergents directly determine the Hurwitz constant of Diop...

Kiister, G., On the Hurwitz product of formal power series and automata, Theoretical Computer Science 83 (1991) 261-273. The Hurwitz (shuffle) product defined on formal power series is generalized to matrices and therefore to automata. The resulting constructions are then used to study commutative power series and abstract families of power series. In particular, the families of power series re...

Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada Department of Applied Mathematics, Donghua University, Shanghai, People’s Republic of China Department of Mathematics, M. P. University of Agriculture and Technology, Rajasthan, India *Corresponding author: [email protected] Received September 15, 2013; Revised October 22, 2013; Accepted Nov...

In this paper we study the reduction of Galois covers of curves, from characteristic zero to positive characteristic. The starting point is a recent result of Raynaud, which gives a criterion for good reduction for covers of the projective line branched at three points. We use the ideas of Raynaud to study the case of covers of the projective line branched at four points. Under some condition o...

Abstract. The semisimple Frobenius manifolds related to the Hurwitz spaces Hg,N(k1, . . . , kl) are considered. We show that the corresponding isomonodromic tau-function τI coincides with (−1/2)power of the Bergmann tau-function which was introduced in a recent work by the authors [8]. This enables us to calculate explicitly the G-function of Frobenius manifolds related to the Hurwitz spaces H0...

Computer vision needs suitable methods of shape representation and contour reconstruction. One of them called method of Hurwitz-Radon Matrices (MHR) can be used in representation and reconstruction of shapes of the objects in the plane. Another problem is connected with shape coefficients. This paper contains the way of length estimation and area estimation via MHR method. Proposed method is ba...

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 non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this qanalogue. All the discussion developed here is entirely ...

Let Z3 act on C by non-trivial opposite characters. Let X = [C/Z3] be the orbifold quotient, and let Y be the unique crepant resolution. We show the equivariant genus 0 Gromov-Witten potentials FX and F are equal after a change of variables — verifying the Crepant Resolution Conjecture for the pair (X , Y ). Our computations involve Hodge integrals on trigonal Hurwitz spaces which are of indepe...