We present several asymptotic analyses for quantities associated with the Riemann and Hurwitz zeta functions. We first determine the leading asymptotic behavior of the Stieltjes constants γk(a). These constants appear in the regular part of the Laurent expansion of the Hurwitz zeta function. We then use asymptotic results for the Laguerre polynomials Ln to investigate a certain sum Sγ(n) involv...

A Popov criterion is derived for systems with slowly timevarying parameters. The parameters and their time derivatives are assumed to take values in convex polytopes.

Many problems start with two (compact Riemann surface) covers f : X → Pz and g : Y → Pz of the Riemann sphere, Pz, uniformized by a variable z. Some data problems have f and g defined over a number field K, and ask: What geometric relation between f and g hold if they map the values X(OK/p) and Y (OK/p) similarly for (almost) all residue classes of OK/p. Variants on Davenport’s problem interpre...

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...

In 1826 N. Abel found a generalization of the binomial formula. In 1902 Abel’s theorem was further generalized by A. Hurwitz. In this paper we describe constructions that provide infinitely many identities each being a generalization of a Hurwitz’s identity. Moreover, we give combinatorial interpretations of all these identities as the forest volumes of certain directed graphs. Published by Els...

A new condition for a polynomial ( ) to be a local convex direction for a Hurwitz stable polynomial ( ) is derived. The condition is in terms of polynomials associated with the even and odd parts of ( ) and ( ), and constitutes a generalization of Rantzer’s phase-growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polyno...

We calculate the cycle class of the Hurwitz divisor D2 on Mg for g = 2k given by the degree k+1 covers of P with simple ramification points, two of which lie in the same fibre. We also study some aspects of the geometry of the natural map from the Hurwitz space H2k,k+1 to the moduli space M2k .

We calculate the cycle class of the Hurwitz divisor D2 on Mg for g = 2k given by the degree k+1 covers of P with simple ramification points, two of which lie in the same fibre. We also study some aspects of the geometry of the natural map from the Hurwitz space H2k,k+1 to the moduli space M2k .