Let f be a smooth function on the unit n-dimensional ball, with the C0-norm, equal to one. We prove that if for some k ⩾ 2, the norm of the kth derivative of f is bounded by 2-k - 1, then the set of ...

We prove some results concerning the behaviour of zeros of families of paraorthogonal polynomials on the unit circle. We establish an interlacing property of the zeros of some functions related to the ...

Random analytic functions are a fundamental object of study in modern complex analysis and probability theory. These functions, often defined through power series with random coefficients, exhibit ...

Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams. Credit: Max Planck Institute for Mathematics in the Sciences How can the behavior of elementary particles ...