The Darmon-Dasgupta units over genus fields and the Shimura correspondence |
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Authors: | Jeehoon Park |
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Institution: | Department of Mathematics, McGill Univ., Montreal, QC, Canada H3A 2K6 |
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Abstract: | We study a special case of the Gross-Stark conjecture (Gross, 1981 Gr]), namely over genus fields. Based on the same idea we provide evidence of the rationality conjecture of the elliptic units for real quadratic fields over genus fields, which is a refinement of the Gross-Stark conjecture given by Darmon and Dasgupta (2006) DD]. Then a relationship between these units and the Fourier coefficients of p-adic Eisenstein series of half-integral weight is explained. |
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Keywords: | Elliptic units for real quadratic fields Gross-Stark conjecture Genus fields |
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