ALGEBRAIC THETA FUNCTIONS AND THE p-ADIC INTERPOLATION OF EISENSTEIN-KRONECKER NUMBERS
نویسندگان
چکیده
We study the properties of Eisenstein-Kronecker numbers, which are related to special values of Hecke L-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 Poincaré bundle of an elliptic curve. We introduce general methods to study the algebraic and p-adic properties of reduced theta functions for CM abelian varieties. As a corollary, when the prime p is ordinary, we give a new construction of the two-variable p-adic measure interpolating special values of Hecke L-functions of imaginary quadratic fields, originally constructed by Manin-Vishik and Katz. Our method via theta functions also gives insight for the case when p is supersingular. The method of this paper will be used in subsequent papers in constructing certain two-variable p-adic distribution for supersingular p interpolating Eisenstein-Kronecker numbers in two-varibales, as well as explicit calculation in two-variables of the p-adic elliptic polylogarithms for CM elliptic curves.
منابع مشابه
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 L-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 Poincaré bundle of an elliptic curve. We introduce general methods to study the algebraic and p-adic proper...
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