P-adic elliptic polylogarithm, p-adic eisenstein series and Katz measure

Kenichi Bannai, Guido Kings

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The specializations of the motivic elliptic polylogarithm on the universal elliptic curve to the modular curve are referred to as Eisenstein classes. In this paper, we prove that the syntomic realization of the Eisenstein classes restricted to the ordinary locus of the modular curve may be expressed using p-adic Eisenstein series of negative weight, which are p-adic modular forms defined using the two-variable p-adic measure with values in p-adic modular forms constructed by Katz. The motivation of our research is the p-adic Beilinson conjecture formulated by Perrin-Riou.

Original languageEnglish
Pages (from-to)1609-1654
Number of pages46
JournalAmerican Journal of Mathematics
Volume132
Issue number6
Publication statusPublished - 2010 Dec

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Polylogarithms
Eisenstein Series
P-adic
Modular Curves
Modular Forms
Specialization
Elliptic Curves
Locus

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

P-adic elliptic polylogarithm, p-adic eisenstein series and Katz measure. / Bannai, Kenichi; Kings, Guido.

In: American Journal of Mathematics, Vol. 132, No. 6, 12.2010, p. 1609-1654.

Research output: Contribution to journalArticle

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