22,886 research outputs found
The relevance of primary dealers for public bond issues
We analyze the role of different kinds of primary and secondary market interventions for the government's goal to maximize its revenues from public bond issuances. Some of these interventions can be thought of as characteristics of a "primary dealer system". After all, we see that a primary dealer system with a restricted number of participants may be useful in case of only restricted competition among sufficiently heterogeneous market makers. We further show that minimum secondary market turnover requirements for primary dealers with respect to bond sales seem to be in general more adequate than the definition of maximum bid-ask-spreads or minimum turnover requirements with respect to bond purchases. Moreover, official price management operations are not able to completely substitute for a system of primary dealers. Finally it should be noted that there is in general no reason for monetary compensations to primary dealers since they already possess some privileges with respect to public bond auction
Images of isogeny classes on modular elliptic curves
Let K be a number field and E/K a modular elliptic curve, with modular
parametrization defined over K. The purpose of this note is to
study the images in E of classes of isogenous points in X_0(N).Comment: LaTeX, 2 pages, to appear in Math. Res. Let
Special subvarieties of Drinfeld modular varieties
We explore an analogue of the Andr\'e-Oort conjecture for subvarieties of
Drinfeld modular varieties. The conjecture states that a subvariety of a
Drinfeld modular variety contains a Zariski-dense set of complex multiplication
(CM) points if and only if is a "special" subvariety (i.e. is defined
by requiring additional endomorphisms). We prove this conjecture in two cases.
Firstly when contains a Zariski-dense set of CM points with a certain
behaviour above a fixed prime (which is the case if these CM points lie in one
Hecke orbit), and secondly when is a curve containing infinitely many CM
points without any additional assumptions.Comment: 22 pages, significant rewrit
Sine kernel asymptotics for a class of singular measures
We construct a family of measures on \bbR that are purely singular with
respect to Lebesgue measure, and yet exhibit universal sine-kernel asymptotics
in the bulk. The measures are best described via their Jacobi recursion
coefficients: these are sparse perturbations of the recursion coefficients
corresponding to Chebyshev polynomials of the second kind. We prove convergence
of the renormalized Christoffel-Darboux kernel to the sine kernel for any
sufficiently sparse decaying perturbation
Higher Heegner points on elliptic curves over function fields
Let E be a modular elliptic curve defined over a rational function field k of
odd characteristic. We construct a sequence of Heegner points on E, defined
over a -tower of finite extensions of k, and show that these
Heegner points generate a group of infinite rank. This is a function field
analogue of a result of C.Cornut and V.VatsalComment: 14 Pages, LaTeX; Minor changes made; To appear in Journal of Number
Theor
Ehrhart f*-coefficients of polytopal complexes are non-negative integers
The Ehrhart polynomial of an integral polytope counts the number of
integer points in integral dilates of . Ehrhart polynomials of polytopes are
often described in terms of their Ehrhart -vector (aka Ehrhart
-vector), which is the vector of coefficients of with respect to
a certain binomial basis and which coincides with the -vector of a regular
unimodular triangulation of (if one exists). One important result by
Stanley about -vectors of polytopes is that their entries are always
non-negative. However, recent combinatorial applications of Ehrhart theory give
rise to polytopal complexes with -vectors that have negative entries.
In this article we introduce the Ehrhart -vector of polytopes or, more
generally, of polytopal complexes . These are again coefficient vectors of
with respect to a certain binomial basis of the space of polynomials and
they have the property that the -vector of a unimodular simplicial complex
coincides with its -vector. The main result of this article is a counting
interpretation for the -coefficients which implies that -coefficients
of integral polytopal complexes are always non-negative integers. This holds
even if the polytopal complex does not have a unimodular triangulation and if
its -vector does have negative entries. Our main technical tool is a new
partition of the set of lattice points in a simplicial cone into discrete
cones. Further results include a complete characterization of Ehrhart
polynomials of integral partial polytopal complexes and a non-negativity
theorem for the -vectors of rational polytopal complexes.Comment: 19 pages, 1 figur
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