Let \chi be a primitive real character. We first establish a
relationship between the existence of the Landau-Siegel zero of
L(s,\chi) and the distribution of zeros of the Dirichlet L-function
L(s,\psi), with \psi belonging to a set \Psi of...
A continuous representation of a profinite group induces a
continuous pseudorepresentation, where a pseudorepresentation is
the data of the
characteristic polynomial coefficients. We discuss the geometry of
the resulting map from the moduli formal...
The theorem of the title is that if the L-function L(E,s) of an
elliptic curve E over the rationals vanishes to order r=0 or 1 at
s=1 then the rank of the group of rational rational points of E
equals r and the Tate-Shafarevich group of E is finite...
A few years ago Ichino-Ikeda formulated a quantitative version
of the Gross-Prasad conjecture, modeled after the classical work of
Waldspurger. This is a powerful local-to-global principle which is
very suitable for analytic and arithmetic...
The trace formula has been the most powerful and mainstream tool
in automorphic forms for proving instances of Langlands
functoriality, including character relations. Its generalization,
the relative trace formula, has also been used to prove...
Application of Plancherel's theorem to integral kernels
approximating compact period functionals yields estimates on
(global) automorphic Levi-Sobolev norms of the functionals. The
utility of this viewpoint can be illustrated in reconsideration
of...
Abstract:
Associated to an abelian variety A/K is a Galois representation
which describes the action of the absolute Galois group of K on the
torsion points of A. In this talk, we shall describe how large the
image of this representation can be (in...
We study open-closed orbifold Gromov-Witten invariants of toric
Calabi-Yau 3-orbifolds with respect to Lagrangian branes of
Aganagic-Vafa type. We prove an open mirror theorem which expresses
generating functions of orbifold disk invariants in terms...
We consider Galois cohomology groups over function fields F of
curves that are defined over a complete discretely valued
field.
Motivated by work of Kato and others for n=3, we show that
local-global principles hold for
$H^n(F, Z/mZ(n-1))$ for all...
For an abelian surface A over a number field k, we study the
limiting distribution of the normalized Euler factors of the
L-function of A. Under the generalized Sato-Tate conjecture, this
is equal to the distribution of characteristic...
