23,190 research outputs found
Medium-run macrodynamics and the consensus view of stabilization policy
Policy implications of the present consensus view of stabilization policy depend on specific assumptions with regard to the equilibrium level of production. Thereby, the interpretation of equilibrium output rests on a separation of supply-side and demandside adjustment to macroeconomic shocks promoting a dichotomy of short-term and long-term macrodynamics. In contrast to this, there are several channels that promote procyclical stimulus of aggregate demand and a changing factor utilization to the accumulation and efficiency of an economy’s productive capacity. Medium-run macrodynamics call for a rather endogenous explanation of production capacity and challenge the uniqueness of long-term equilibria.Monetary policy, medium-run macrodynamics, long-term nonneutrality, capacity utilization.
Distributions and Analytic Continuation of Dirichlet Series
This paper is second in a series of three papers; the first of which is
"Summation Formulas, from Poisson and Voronoi to the Present"
(math.NT/0304187), and the third of which is "Automorphic Distributions,
L-functions, and Voronoi Summation for GL(3)". The first paper is primarily an
expository paper, while the third proves a Voronoi-style summation formula for
the coefficients of a cusp form on GL(3,Z)\GL(3,R). This present paper contains
the distributional machinery used in the third paper for rigorously deriving
the summation formula, and also for the proof of the GL(3)xGL(1) converse
theorem given in the third paper. The primary concept studied is a notion of
the order of vanishing of a distribution along a closed submanifold.
Applications are given to the analytic continuation of Riemann's zeta function;
degree 1 and degree 2 L-functions; the converse theorem for GL(2); and a
characterization of the classical Mellin transform/inversion relations on
functions with specified singularities.Comment: 72 page
The Dirac propagator in the Kerr-Newman metric
We give an alternative proof of the completeness of the Chandrasekhar ansatz
for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an
integral representation for smooth compactly supported functions which in turn
we use to derive an integral representation for the propagator of solutions of
the Cauchy problem with initial data in the above class of functions. As a
by-product, we also obtain the propagator for the Dirac equation in the
Minkowski space-time in oblate spheroidal coordinates.Comment: 29 pages, modifications in the abstract and in the introduction,
small improvements in section 2.
Pairings of automorphic distributions
We present a pairing of automorphic distributions that applies in situations
where a Lie group acts with an open orbit on a product of generalized flag
varieties. The pairing gives meaning to an integral of products of automorphic
distributions on these varieties. This generalizes classical integral
representations or "Rankin-Selberg integrals" of L-functions, and gives new
constructions and analytic continuations of automorphic L-functions.
Keywords: Automorphic forms, invariant pairings, automorphic distributions,
L-functions, analytic continuation, rapid decay.Comment: 19 pages, to appear in Mathematische Annale
Automorphic Distributions, L-functions, and Voronoi Summation for GL(3)
This paper is third in a series of three, following "Summation Formulas, from
Poisson and Voronoi to the Present" (math.NT/0304187) and "Distributions and
Analytic Continuation of Dirichlet Series" (math.FA/0403030). The first is
primarily an expository paper explaining the present one, whereas the second
contains some distributional machinery used here as well. These papers concern
the boundary distributions of automorphic forms, and how they can be applied to
study questions about cusp forms on semisimple Lie groups. The main result of
this paper is a Voronoi-style summation formula for the Fourier coefficients of
a cusp form on GL(3,Z)\GL(3,R). We also give a treatment of the standard
L-function on GL(3), focusing on the archimedean analysis as performed using
distributions. Finally a new proof is given of the GL(3)xGL(1) converse theorem
of Jacquet, Piatetski-Shapiro, and Shalika. This paper is also related to the
later papers math.NT/0402382 and math.NT/0404521.Comment: 66 pages, published versio
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