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Explore advanced concepts in number theory through this lecture focusing on degenerate automorphic forms and their connections to Euler systems. Delve into the intricate relationships between automorphic forms and the arithmetic properties of special values of L-functions, examining how these mathematical structures contribute to understanding the Bloch-Kato conjecture. Learn about the role of degenerate automorphic forms in constructing Euler systems, which serve as crucial tools for studying Selmer groups and their connections to L-values. Investigate the theoretical framework that links automorphic representations to algebraic structures such as Chow groups, building upon foundational concepts that extend the classical Birch and Swinnerton-Dyer conjecture. Discover how recent developments in this field have strengthened the connections between automorphic forms and arithmetic geometry, particularly in the context of motives over global fields. Examine the technical aspects of how degenerate cases of automorphic forms provide insights into the broader landscape of L-functions and their special values, contributing to the ongoing research in understanding the arithmetic nature of these fundamental mathematical objects.
