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Explore advanced number theory through this 55-minute conference talk that proves the simultaneous equidistribution conjecture of Michel and Venkatesh for torus embeddings into distinct inner forms of PGL_2. Discover how assuming a strengthened non-existence condition for Siegel zeros of quadratic characters leads to significant improvements over previous analytical and ergodic approaches. Learn about the innovative use of fractional moment bounds for L-functions as essential proof tools and examine connections to Harper's work on random multiplicative functions. Understand how this approach overcomes the limitations of earlier methods by Blomer–Brumley and Aka–Einsiedler–Shapira, which could only cover 99% of discriminants due to double splitting conditions, while this new method addresses essentially all cases with O(1) exceptional characters per dyadic interval.
