Expected Number of Zeros of Random Power Series with Finitely Dependent Gaussian Coefficients

Expected Number of Local Maxima of Some Gaussian Random Polnomials

expected number of local maxima of some gaussian random polnomials

Real Zeros of Algebraic Polynomials with Dependent Random Coefficients

The expected number of real zeros of polynomials a0+a1x+a2x+ · · · + an−1xn−1 with random coefficients is well studied. For n large and for the normal zero mean independent coefficients, irrespective of the distribution of coefficients, this expected number is known to be asymptotic to (2/π) logn. For the dependent cases studied so far it is shown that this asymptotic value remains O(logn). In ...

The Real Zeros of a Random Polynomial with Dependent Coefficients

Abstract. Mark Kac gave one of the first results analyzing random polynomial zeros. He considered the case of independent standard normal coefficients and was able to show that the expected number of real zeros for a degree n polynomial is on the order of 2 π logn, as n → ∞. Several years later, Sambandham considered two cases with some dependence assumed among the coefficients. The first case ...

Zeros of Dirichlet series with periodic coefficients

Let a = (an)n≥1 be a periodic sequence, Fa(s) the meromorphic continuation of P n≥1 an/n , and Na(σ1, σ2, T ) the number of zeros of Fa(s), counted with their multiplicities, in the rectangle σ1 < Re s < σ2, | Im s| ≤ T . We extend previous results of Laurinčikas, Kaczorowski, Kulas, and Steuding, by showing that if Fa(s) is not of the form P (s)Lχ(s), where P (s) is a Dirichlet polynomial and ...