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A -adic version of Stark’s Conjecture at is attributed to J.-P. Serre and stated
(faultily) in Tate’s book on the Conjecture. Building instead on our previous paper (and
work of Rubin) on the complex abelian case, we give a new approach to such a conjecture
for real ray-class extensions of totally real number fields. We study the coherence of
our -adic conjecture and then formulate some integral refinements, both alone and in
combination with its complex analogue. A ‘Weak Combined Refined’ version...
The purpose of this paper is to generalize, to certain commutative formal groups of dimension one and height greater than one defined over the ring of integers of a finite extension of , some results on -adic interpolation developed by Kubota, Leopoldt, Iwasawa, Mazur, Katz and others notably for the multiplicative group , and which they used to construct -adic -functions.
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