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Explore the intricacies of number theory in this seminar talk delivered by Shai Evra from Princeton University at the Joint IAS/Princeton University Number Theory Seminar. Delve into the evolution of the Ramanujan Conjecture, examining its various forms including the Generalized Ramanujan Conjecture (GRC) and the Generalized Ramanujan-Peterson Conjecture (GRPC). Investigate the Samak-Xue Density Hypothesis (SXDH) and its implications. Gain insights into the automorphic classification of general linear and classical groups, as well as the concept of automorphic genus. Examine key claims and examples, with a focus on a main example that illustrates the discussed concepts.
