### 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 language | English |
---|---|

Pages (from-to) | 1609-1654 |

Number of pages | 46 |

Journal | American Journal of Mathematics |

Volume | 132 |

Issue number | 6 |

Publication status | Published - 2010 Dec |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*American Journal of Mathematics*,

*132*(6), 1609-1654.

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

Research output: Contribution to journal › Article

*American Journal of Mathematics*, vol. 132, no. 6, pp. 1609-1654.

}

TY - JOUR

T1 - P-adic elliptic polylogarithm, p-adic eisenstein series and Katz measure

AU - Bannai, Kenichi

AU - Kings, Guido

PY - 2010/12

Y1 - 2010/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78650875307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650875307&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:78650875307

VL - 132

SP - 1609

EP - 1654

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

IS - 6

ER -