This article can be read as a companion and sequel to [DLR], which proposes aconjectural expression for the so-called p-adic iterated integrals attached to a triple (f, g, h)of classical eigenforms of weights (2, 1, 1). When f is a cusp form, this expression involvesthe p-adic logarithms of so-called Stark points: distinguished points on the modular abelianvariety attached to f, defined over the number field cut out by the Artin representationsattached to g and h. The goal of this paper is to formulate an analogous conjecture when fis a weight two Eisenstein series rather than a cusp form. The resulting formula involves thep-adic logarithms of units and p-units in suitable number fields, and can be seen as a newvariant of Gross’s p-adic analogue of Stark’s conjecture on Artin L-series at s = 0.
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