**Papers Published**

- Dasgupta, S; Darmon, H; Pollack, R,
*Hilbert modular forms and the Gross-Stark conjecture*, Annals of Mathematics, vol. 174 no. 1 (July, 2011), pp. 439-484, Annals of Mathematics, Princeton U

(last updated on 2019/06/20)**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.