Gross-Stark units and p-adic iterated integrals attached to modular forms of weight one
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This article can be read as a companion and sequel to the authors’ earlier article on Stark points and p-adic iterated integrals attached to modular forms of weight one, which proposes a conjectural 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 involves the p-adic logarithms of so-called Stark points: distinguished points on the modular abelian variety attached to f, defined over the number field cut out by the Artin representations attached to g and h. The goal of this paper is to formulate an analogous conjecture when f is a weight two Eisenstein series rather than a cusp form. The resulting formula involves the p-adic logarithms of units and p-units in suitable number fields, and can be seen as a new variant of Gross’s p-adic analogue of Stark’s conjecture on Artin L-series at s=0 .
The final publication is available at Springer via http://dx.doi.org/10.1007/s40316-015-0042-6
CitationDarmon, H., Lauder, A., Rotger, V. Gross-Stark units and p-adic iterated integrals attached to modular forms of weight one. "Annales mathématiques du Québec", 1 Agost 2016, vol. 40, núm. 2, p. 325-354.