Article ID Journal Published Year Pages File Type
5778347 Advances in Mathematics 2017 16 Pages PDF
Abstract
We characterize the limiting distribution of Rudin-Shapiro polynomials, showing that, normalized, their values become uniformly distributed in the disc. This resolves conjectures of Saffari and Montgomery. Our proof proceeds by relating the polynomials' distribution to that of a product of weakly dependent random matrices, which we analyze using the representation theory of SU(2). Our approach leads us to a non-commutative analogue of the classical central limit theorem of Salem and Zygmund, which may be of independent interest.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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