Math @ Duke
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Publications [#338516] of Samit Dasgupta
Papers Published
- Dasgupta, S; Darmon, H; Pollack, R, Hilbert modular forms and the Gross-Stark conjecture,
Annals of Mathematics, vol. 174 no. 1
(January, 2011),
pp. 439-484, Annals of Mathematics, Princeton U [doi]
(last updated on 2024/04/19)
Abstract: Let F be a totally real field and χ an abelian totally odd character of F. In 1988, Gross stated a p-adic analogue of Stark's conjecture that relates the value of the derivative of the p-adic L-function associated to χ and the p-adic logarithm of a p-unit in the extension of F cut out by χ. In this paper we prove Gross's conjecture when F is a real quadratic field and χ is a narrow ring class character. The main result also applies to general totally real fields for which Leopoldt's conjecture holds, assuming that either there are at least two primes above p in F, or that a certain condition relating the L-invariants of χ and χ-1 holds. This condition on L-invariants is always satisfied when χ is quadratic.
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