- The Kronecker limit formulas via the distribution relation
- joint work with Shinichi Kobayashi
- Preprint 2008, arXiv:0807.4008v1 [math.NT]
**Abstract.**
In this paper, we give a proof of the classical Kronecker limit formulas using the distribution
relation of the Eisenstein-Kronecker series. Using a similar idea, we then prove *p*-adic
analogues of the Kronecker limit formulas for the
*p*-adic Eisenstein-Kronecker functions defined in our previous paper.

*p*-adic Eisenstein-Kronecker functions and the elliptic polylogarithm for CM elliptic curves
- joint work with
Hidekazu Furusho and
Shinichi Kobayashi
- Preprint 2008, arXiv:0807.4007v1 [math.NT]
**Abstract.**
In this paper, we construct a *p*-adic analogue of the Eisenstein-Kronecker series
as a Coleman function on an elliptic curve with complex multiplication.
We then show that the periods of the specialization of the *p*-adic elliptic polylogarithm sheaf
to arbitrary points of the elliptic curve may be expressed using this function.

- Integral structures on
*p*-adic Fourier theory
- joint work with Shinichi Kobayashi
- Preprint 2008, arXiv:0804.4338v2 [math.NT]
**Abstract.**
In this article, we study integral structures on *p*-adic Fourier theory by Schneider and Teitelbaum.
As an application of our result, we give a certain integral basis of the space of *K*-locally analytic functions
for any finite extension *K* of **Q**_{p}, generalizing the basis of Amice of locally analytic functions on
**Z**_{p}.
We also use our result to prove congruences of Bernoulli-Hurwitz numbers at supersingular primes
originally investigated by Katz and Chellali.