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7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also
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This text (together with a forthcoming second volume) presents most of the courses and seminars delivered at the meeting entitled "Frontiers in number theory, p
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In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems,