Iwasawa theory and p-adic L-functions over ${\mathbb Z}_{p}^{2}$-extensions

p-adic L-functions over the false Tate curve extensions

Let f be a primitive modular form of CM type of weight k and level 0(N ). Let p be an odd prime which does not divide N , and for which f is ordinary. Our aim is to padically interpolate suitably normalized versions of the critical values L( f, ρχ, n), where n = 1, 2, . . . , k − 1, ρ is a fixed self-dual Artin representation of M∞ defined by (1·1) below, and χ runs over the irreducible Artin r...

Iwasawa theory of overconvergent modular forms, I: Critical-slope p-adic L-functions

We construct an Euler system of p-adic zeta elements over the eigencurve which interpolates Kato’s zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable p-adic L-function over the eigencurve. As a first application of these ideas, we prove the equality of the p-adic L-functions associated with a critical-slope refin...

Iwasawa Theory and Motivic L-functions

We illustrate the use of Iwasawa theory in proving cases of the (equivariant) Tamagawa number conjecture.

p-adic unit roots of L-functions over finite fields

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a question in arithmetic mirror symmetry.

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