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A p-adic analogue of Siegel's theorem on sums of squares
Jeudi, 22 Mars, 2018 - 10:30
Résumé : 

Every positive rational number is the sum of four squares by a well-known theorem of Euler. As predicted by Hilbert and proven by Siegel, this generalizes to arbitrary number fields K when one replaces 'positive' by 'totally positive', i.e. positive with respect to every embedding of K into the reals. I will motivate and present a p-adic analogue of this, which gives a constructive description of those elements of K that are totally p-adically integral, i.e. p-adic integers for each embedding of K into the p-adic numbers. The proof of this result involves the Brauer-Hasse-Noether local-global principle for central simple algebras. Joint work with Sylvy Anscombe and Philip Dittmann.

Institution de l'orateur : 
Thème de recherche : 
Théorie des nombres
Salle : 
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