Differentiation Evens out Zero Spacings
نویسندگان
چکیده
Abstract. Suppose f(x) is a polynomial with all of its roots on the real line. We show that the roots of f (x) are more evenly spaced than the roots of f(x). The same holds for polynomials with all their zeros on a circle, as well as an entire function of order 1 with all its zeros on a line. Applications are given to the Riemann zeta-function and its connection to random matrix polynomials. We also obtain a new proof that ζ(2) = π/6.
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