360 research outputs found
Families of L-functions and their Symmetry
In [90] the first-named author gave a working definition of a family of
automorphic L-functions. Since then there have been a number of works [33],
[107], [67] [47], [66] and especially [98] by the second and third-named
authors which make it possible to give a conjectural answer for the symmetry
type of a family and in particular the universality class predicted in [64] for
the distribution of the zeros near s=1/2. In this note we carry this out after
introducing some basic invariants associated to a family
Notes on an analogue of the Fontaine-Mazur conjecture
We estimate the proportion of function fields satisfying certain conditions
which imply a function-field analogue of the Fontaine-Mazur conjecture. As a
byproduct, we compute the fraction of abelian varieties (or even Jacobians)
over a finite field which have a rational point of order l.Comment: 12 pages; minor revisions according to referees' comment
The distribution of class groups of function fields
Using equidistribution results of Katz and a computation in finite symplectic
groups, we give an explicit asymptotic formula for the proportion of curves C
over a finite field for which the l-torsion of Jac(C) is isomorphic to a given
abelian l-group. In doing so, we prove a conjecture of Friedman and WashingtonComment: To appear, JPA
Bifurcation currents and equidistribution on parameter space
In this paper we review the use of techniques of positive currents for the
study of parameter spaces of one-dimensional holomorphic dynamical systems
(rational mappings on P^1 or subgroups of the Moebius group PSL(2,C)). The
topics covered include: the construction of bifurcation currents and the
characterization of their supports, the equidistribution properties of
dynamically defined subvarieties on parameter space.Comment: Revised version, 46 pages, to appear in the proceedings of the
conference "Frontiers in complex dynamics (Celebrating John Milnor's 80th
birthday)
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