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Explore advanced concepts in number theory through this lecture examining degenerate automorphic forms and their relationship to Euler systems. Delve into the intricate connections between automorphic forms and the arithmetic properties of special values of L-functions, building upon foundational knowledge from previous lectures in this series. Investigate how degenerate cases of automorphic forms contribute to our understanding of the Bloch-Kato conjecture and its generalizations of the Birch and Swinnerton-Dyer conjecture. Examine the role of Euler systems as powerful tools for studying orders of algebraic structures such as Chow groups and Selmer groups. Analyze the theoretical framework connecting L-values to arithmetic objects through the lens of automorphic representations over global fields. Gain insights into recent developments in this active area of research that bridges algebraic number theory, arithmetic geometry, and the theory of automorphic forms, presented as part of a comprehensive program on automorphic forms and the Bloch-Kato conjecture at the International Centre for Theoretical Sciences.
