Mathematics Colloquia and Seminars

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One seemingly innocent reformulation of the Riemann Hypothesis is the Nyman–Beurling criterion — an approximation problem in L2 involving dilations of the fractional part function. Introducing randomness into these dilations leads to new criteria and structures.  These are connected to a range of objects and problems, such as period functions associated with Eisenstein series,  moment problems in measure theory for weighted mean squares of the Riemann zeta function or Dirichlet L-functions, and higher moments of zeta. The talk will be accessible to a broad audience. Joint works with F. Alouges, E. Hillion, J. Najnudel, B. Ringeling, and E. Royer.