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On common roots of Legendre polynomials

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GST - Geometric spectral theory and applications

It was shown by Bourgain and Rudnick in 2010 that for a curve of non-vanishing curvature on the standard flat 2-torus there are no eigenfunctions of arbitrarily large eigenvalues which vanish on it.  We show that for any small circle on the 2-sphere there are no  zonal spherical harmonics of arbitrarily large eigenvalues which  vanish on it. Equivalently, only  a finite number of Legendre polynomials can share a  non-zero root. The conjecture by Stieltjes is that Legendre polynomials have no common non-zero roots. The talk is based on joint works with Adi Weller Weiser and Borys Kadets.

This talk is part of the Isaac Newton Institute Seminar Series series.

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