BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
نویسنده
چکیده
The romance of analysis and arithmetic is among the deepest and most enticing themes in all of mathematics. Though arithmetic, with all of its delicate subtleties, may at first seem an unlikely match for analysis with its powerful techniques, the relationship between the two has always been a vital one. In recent decades padic analysis—a hybrid of arithmetic and analysis—has emerged as a fascinating offspring of this union. With stunning successes in Iwasawa theory, p-adic modular forms, p-adic galois representations and their deformation theory, the field of padic analysis has forcefully asserted its own independence. Perhaps even more significantly, the p-adic theory is beginning to reveal some of the most intimate secrets of the mysterious relationship of analysis and arithmetic. Andrew Wiles’s recent proof with Richard Taylor [12], [13] of the semistable modularity conjecture— and its corollary, Fermat’s Last Theorem—is just one striking example. Among the most successful tools for the interaction of analysis and arithmetic are the Dirichlet series, i.e. infinite series of the form
منابع مشابه
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
Representations of semisimple Lie algebras in the BGG category í µí²ª, by James E.
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