Maksym Radziwill: Joint Linnik Problems and Siegel Zeros (September 11, 2025)

We prove the simultaneous equidistribution conjecture of Michel and Venkatesh for the embedding of a torus into two distinct inner forms of PGL_2 assuming a o(1) strengthening of the non-existence of Siegel zeros for quadratic characters. Uploaded 25-09-25 Since the number of such exceptional characters is essentially O(1) per dyadic interval, our approach improves the previous analytic approach of Blomer–Brumley and the ergodic Aka–Einsiedler–Shapira approach, which covers at best 99% discriminants in [X, 2X] due to a double splitting condition. The relevance of this topic to the workshop is that an essential tool in the proof are bounds for fractional moments of L-functions; in fact, we uncover a non-trivial intersection with the work of Harper on random multiplicative functions, but we end up not needing it at the end of the day for our specific application (although it would be needed for certain generalizations of our result). For more information go here: https://www.simonsfoundation.org/event/mps-conference-on-universal-statistics-in-number-theory/