JournalscmhVol. 87, No. 1pp. 71–111

Height pairings, exceptional zeros and Rubin’s formula: the multiplicative group

  • Kâzim Büyükboduk

    Koç University, Istanbul, Turkey
Height pairings, exceptional zeros and Rubin’s formula:  the multiplicative group cover
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Abstract

In this paper we prove a formula, much in the spirit of one due to Rubin, which expresses the leading coefficients of various pp-adic LL-functions in the presence of an exceptional zero in terms of Nekovář’s pp-adic height pairings on his extended Selmer groups. In a particular case, the Rubin-style formula we prove recovers a pp-adic Kronecker limit formula. In a disjoint case, we observe that our computations with Nekovář’s heights agree with the Ferrero–Greenberg formula (more generally, Gross’ conjectural formula) for the leading coefficient of the Kubota–Leopoldt pp-adic LL-function (resp., the Deligne–Ribet pp-adic LL-function) at s=0s=0.

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Kâzim Büyükboduk, Height pairings, exceptional zeros and Rubin’s formula: the multiplicative group. Comment. Math. Helv. 87 (2012), no. 1, pp. 71–111

DOI 10.4171/CMH/249