P. Buser and P. Sarnak constructed Riemann surfaces whose systole behaves logarithmically in the genus. The Fuchsian groups in their examples are principal congruence subgroups of a fixed arithmetic group with rational trace field. We generalize their construction to principal congruence subgroups of arbitrary arithmetic surfaces. The key tool is a new trace estimate valid for an arbitrary idea...

Space-time block codes from orthogonal designs recently proposed by Alamouti, and TarokhJafarkhani-Calderbank have attracted considerable attention due to the fast maximum-likelihood (ML) decoding and the full diversity. There are two classes of space-time block codes from orthogonal designs. One class consists of those from real orthogonal designs for real signal constellations which have been...

Consider the Hurwitz space parameterizing covers of P branched at four points. We study its intersection with divisor classes on the moduli space of curves. As applications, we calculate the slope of Teichmüller curves parameterizing square-tiled cyclic covers. In addition, we come up with a relation among the slope of Teichmüller curves, the sum of Lyapunov exponents and the Siegel-Veech const...

The results of two kinds of studies show PA develops on its own in first language development, without instruction: (1) children in comparison groups in PA training studies, who get no PA training, typically improve in PA (Ehri, Nunes, Willows, Schuster, Yaghoub-Zadehm and Shanahan, 2001, p. 276); (2) longitudinal studies show that nearly all children score very well on tests of PA by about gra...

We show that L 4 and L 5 in the spatial restricted circular three{body problem are Nekhoroshev{ stable for all but a few values of the reduced mass up to the Routh critical value. This result is based on two extensions of previous results on Nekhoroshev{stability of elliptic equilibria, namely to the case of`directional quasi{convexity', a notion introduced here, and to a (non-convex) steep cas...

In this paper, which is a companion paper to W , starting from the Euler integral which appears in a generalization of Jensen’s formula, we shall give a closed form for the integral of log Γ 1± t . This enables us to locate the genesis of two new functions A1/a and C1/a considered by Srivastava and Choi. We consider the closely related function A(a) and the Hurwitz zeta function, which render t...

We study the equivariant Gromov-Witten theory of a rank 2 vector bundle N over a nonsingular curve X of genus g: (i) We define a TQFT using the Gromov-Witten partition functions. The full theory is determined in the TQFT formalism from a few exact calculations. We use a reconstruction result proven jointly with C. Faber and A. Okounkov in the appendix. X and N is equipped with the anti-diagonal...

In this paper we study the Hurwitz scheme in terms of the Sato Grassmannian and the algebro-geometric theory of solitons. We will give a characterization, its equations and a show that there is a group of Virasoro type which uniformizes it.

A system of m nonzero vectors in Zn is called an m-icube if they are pairwise orthogonal and have the same length. The paper describes m-icubes in Z for 2 ≤ m ≤ 4 using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in Z.

Every finite group acts as the full isometry group of some compact hyperbolic 3-manifold. In this paper we study those finite groups which act maximally, that is when the ratio |Isom(M)|/vol(M) is maximal among all such manifolds. In two dimensions maximal symmetry groups are called Hurwitz groups, and arise as quotients of the (2,3,7)–triangle group. Here we study quotients of the minimal co-v...