Leading terms of anticyclotomic Stickelberger elements and $p$-adic periods

Anticyclotomic p-adic L-functions and Ichino’s formula

We give a new construction of a p-adic L-function L(f,Ξ), for f a holomorphic newform and Ξ an anticyclotomic family of Hecke characters of Q( √ −d). The construction uses Ichino’s triple product formula to express the central values of L(f, ξ, s) in terms of Petersson inner products, and then uses results of Hida to interpolate them. The resulting construction is well-suited for studying what ...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

p-ADIC HEIGHTS OF HEEGNER POINTS AND ANTICYCLOTOMIC Λ-ADIC REGULATORS

Let E be an elliptic curve defined over Q. The aim of this paper is to make it possible to compute Heegner L-functions and anticyclotomic Λ-adic regulators of E, which were studied by Mazur-Rubin and Howard. We generalize results of Cohen and Watkins, which enable us to compute Heegner points of non-fundamental discriminant. We then prove a relationship between the denominator of a point of E d...

Irrationality of Certain p - adic Periods for Small p

Apéry’s proof [13] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significant new results (although further progress has been made on the irrationality of zeta values [1, 14]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and Lege...

p-ADIC PERIODS AND DERIVED DE RHAM COHOMOLOGY

For a smooth variety X over a base field of characteristic 0 we have its algebraic de Rham cohomology H · dR(X) := H (XZar,Ω · X); for nonsmooth X, one defines H · dR(X) using cohomological descent as in Deligne [D]. If the base field is C, then one has the Betti cohomology H · B(X) := H (Xcl,Q) and a canonical period isomorphism (“integration of algebraic differential forms over topological cy...