1,897 research outputs found
Nonvanishing of twists of -functions attached to Hilbert modular forms
We describe algorithms for computing central values of twists of
-functions associated to Hilbert modular forms, carry out such computations
for a number of examples, and compare the results of these computations to some
heuristics and predictions from random matrix theory.Comment: 19 page
Compactifications of moduli spaces inspired by mirror symmetry
We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds,
using the one-loop semiclassical approximation. The data being parameterized
includes a choice of complex structure on the manifold, as well as some ``extra
structure'' described by means of classes in H^2. The expectation that this
moduli space is well-behaved in these ``extra structure'' directions leads us
to formulate a simple and compelling conjecture about the action of the
automorphism group on the K\"ahler cone. If true, it allows one to apply
Looijenga's ``semi-toric'' technique to construct a partial compactification of
the moduli space. We explore the implications which this construction has
concerning the properties of the moduli space of complex structures on a
``mirror partner'' of the original Calabi-Yau manifold. We also discuss how a
similarity which might have been noticed between certain work of Mumford and of
Mori from the 1970's produces (with hindsight) evidence for mirror symmetry
which was available in 1979. [The author is willing to mail hardcopy preprints
upon request.]Comment: 25 pp., LaTeX 2.09 with AmS-Font
Algebraic Coset Conformal field theories
All unitary Rational Conformal Field Theories (RCFT) are conjectured to be
related to unitary coset Conformal Field Theories, i.e., gauged
Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use
subfactor theory and ideas of algebraic quantum field theory to approach coset
Conformal Field Theories. Two conjectures are formulated and their consequences
are discussed. Some results are presented which prove the conjectures in
special cases. In particular, one of the results states that a class of
representations of coset () algebras with critical parameters
are irreducible, and under the natural compositions (Connes' fusion), they
generate a finite dimensional fusion ring whose structure constants are
completely determined, thus proving a long-standing conjecture about the
representations of these algebras.Comment: 49 pages, Improved presentations and added details, to appear in
Comm.Math.Phy
Explicit methods for Hilbert modular forms
We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of
Hilbert modular forms over a totally real field. We provide many explicit
examples as well as applications to modularity and Galois representations.Comment: 52 pages, 10 figures, many table
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