Decoupling for short generalized Dirichlet sequences

Abstract: We will discuss some geometric similarities between the sequence $\{\log n\}_{n=N+1}^{N+N^{1/2}}$ (and sequences with similar convexity properties) and the parabola from a decoupling point of view. Based on those observations we present decoupling inequalities for those sequences. The sequence $\{\log n\}_{n=N+1}^{2N}$ is closely connected to a conjecture of Montgomery on Dirichlet polynomials but we see some difficulties in studying the sequence $\{\log n\}_{n=N+1}^{N+N^{\alpha}}$ for $\alpha > 1/2$. This is joint work with Larry Guth and Dominique Maldague.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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