Math @ Duke

Publications [#338516] of Samit Dasgupta
Papers Published
 Dasgupta, S; Darmon, H; Pollack, R, Hilbert modular forms and the GrossStark conjecture,
Annals of Mathematics, vol. 174 no. 1
(January, 2011),
pp. 439484, Annals of Mathematics, Princeton U [doi]
(last updated on 2022/01/25)
Abstract: Let F be a totally real field and χ an abelian totally odd character of F. In 1988, Gross stated a padic analogue of Stark's conjecture that relates the value of the derivative of the padic Lfunction associated to χ and the padic logarithm of a punit 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 Linvariants of χ and χ1 holds. This condition on Linvariants is always satisfied when χ is quadratic.


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