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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 Qp, generalizing the basis of Amice of locally analytic functions on Zp. We also use our result to prove congruences of Bernoulli-Hurwitz numbers at supersingular primes originally investigated by Katz and Chellali.