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Irregular Weight One Points with
$D_{4}$ Image
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 1 / March 2019
- Published online by Cambridge University Press:
- 04 January 2019, pp. 109-118
- Print publication:
- March 2019
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- Article
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Darmon, Lauder, and Rotger conjectured that the relative tangent space of an eigencurve at a classical, ordinary, irregular weight one point is of dimension two. This space can be identified with the space of normalized overconvergent generalized eigenforms, whose Fourier coefficients can be conjecturally described explicitly in terms of
$p$-adic logarithms of algebraic numbers. This article presents the proof of this conjecture in the case where the weight one point is the intersection of two Hida families of Hecke theta series.
