210 research outputs found
Robert F. Coleman 1954-2014
Robert F. Coleman, a highly original mathematician who has had a profound
influence on modern number theory and arithmetic geometry, passed away on March
24, 2014. We give an overview of his life and career, including some of his
major contributions to mathematics and his role as an activist and spokesperson
for people with disabilities.Comment: 14 pages. v2: Some minor typos correcte
Recommended from our members
Modular Forms
The theory of Modular Forms has been central in mathematics with a
rich history and connections to many other areas of mathematics. The
workshop explored recent developments and future directions with a
particular focus on connections to the theory of periods
Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers
We study the properties of Eisenstein-Kronecker numbers, which are related to
special values of Hecke -function of imaginary quadratic fields. We prove
that the generating function of these numbers is a reduced (normalized or
canonical in some literature) theta function associated to the Poincare bundle
of an elliptic curve. We introduce general methods to study the algebraic and
-adic properties of reduced theta functions for CM abelian varieties. As a
corollary, when the prime is ordinary, we give a new construction of the
two-variable -adic measure interpolating special values of Hecke
-functions of imaginary quadratic fields, originally constructed by
Manin-Vishik and Katz. Our method via theta functions also gives insight for
the case when is supersingular. The method of this paper will be used in
subsequent papers to study the precise -divisibility of critical values of
Hecke -functions associated to Hecke characters of quadratic imaginary
fields for supersingular , as well as explicit calculation in two-variables
of the -adic elliptic polylogarithm for CM elliptic curves.Comment: 55 pages, 2 figures. Minor misprints and errors were correcte
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