210 research outputs found

    Robert F. Coleman 1954-2014

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    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

    Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers

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    We study the properties of Eisenstein-Kronecker numbers, which are related to special values of Hecke LL-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 pp-adic properties of reduced theta functions for CM abelian varieties. As a corollary, when the prime pp is ordinary, we give a new construction of the two-variable pp-adic measure interpolating special values of Hecke LL-functions of imaginary quadratic fields, originally constructed by Manin-Vishik and Katz. Our method via theta functions also gives insight for the case when pp is supersingular. The method of this paper will be used in subsequent papers to study the precise pp-divisibility of critical values of Hecke LL-functions associated to Hecke characters of quadratic imaginary fields for supersingular pp, as well as explicit calculation in two-variables of the pp-adic elliptic polylogarithm for CM elliptic curves.Comment: 55 pages, 2 figures. Minor misprints and errors were correcte
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