Degeneration of polylogarithms and special values of L-functions for totally real fields
نویسنده
چکیده
The degeneration of the polylogarithm on the universal abelian scheme over a Hilbert modular variety at the boundary is described in terms of (critical) special values of the L-function of the totally real field defining the variety. This gives a relation between the polylogarithm on abelian schemes and special values of L-functions. 2000 Mathematics Subject Classification: 11F41, 11G55, 11R42
منابع مشابه
Hecke Characters and the K–theory of Totally Real and Cm Number Fields
Let F/K be an abelian extension of number fields with F either CM or totally real and K totally real. If F is CM and the BrumerStark conjecture holds for F/K, we construct a family of G(F/K)–equivariant Hecke characters for F with infinite type equal to a special value of certain G(F/K)–equivariant L–functions. Using results of Greither–Popescu [19] on the Brumer–Stark conjecture we construct l...
متن کاملComputing p-adic L-functions of totally real number fields
We prove new explicit formulas for the p-adic L-functions of totally real number fields and show how these formulas can be used to compute values and representations of p-adic L-functions.
متن کاملComputing Special Values of Partial Zeta Functions
We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the Eisenstein cocycle Ψ , a group cocycle for GLn(Z); the special values are computed as periods of Ψ , and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for cubic and quartic fields of small discriminant.
متن کاملEvaluation of Dedekind Sums, Eisenstein Cocycles, and Special Values of L-functions
We define certain higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums, and show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications. First, we show how to express special values of partial zeta functions associated to totally real number fields in terms of these sums via the Eisenstein cocycl...
متن کاملALGEBRAIC THETA FUNCTIONS AND THE 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...
متن کامل