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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...
On décrit un problème naturel concernant la transformation de Fourier. Soient , deux fonctions associées par celle-ci, positives pour et nulles en zéro. Quelle est la borne inférieure pour ? En dimension supérieure, même question, l’intervalle étant remplacé par la boule de rayon . On montre l’existence d’une borne inférieure strictement positive, qui est estimée en fonction de la dimension. La dernière section montre que cette question est naturellement liée à la théorie des fonctions zêta....
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