Complex zeros of cylinder functions

The Real Zeros of the Derivatives of Cylinder Functions of Negative Order

We study the real x–zeros of the derivative C ν (x) of the cylinder function Cν(x) = Cν(x, α) = cosαJν(x) − sinαYν(x) for ν < 0. For fixed α, 0 ≤ α < π and n = 1, 2, . . ., we show the existence of a number νn in the interval −n+ α/π − 1 < ν < −n+ α/π such that the first positive zero of C ν (x) occurs after the first positive zero of Cν(x) when −n− 1 + α/π < ν < νn and before the first positiv...

Complex Zeros of Two Incomplete Riemann Zeta Functions

The computation of the complex zeros of an incomplete Riemann zeta function defined in an earlier paper is extended and new zero trajectories are given. A second incomplete Riemann zeta function is denned and its zero trajectories are investigated numerically as functions of the upper limit X of the definition integral. It becomes apparent that there exist three different classes of zero trajec...

Absence of zeros and asymptotic error estimates for Airy and parabolic cylinder functions

Zeros of complex caloric functions and singularities of complex viscous Burgers equation

We show that the viscous Burgers equation ut+uux = uxx considered for complex valued functions u develops finite-time singularities from compactly supported smooth data. By means of the Cole-Hopf transformation, the singularities of u are related to zeros of complexvalued solutions v of the heat equation vt = vxx. We prove that such zeros are isolated if they are not present in the initial data.

Zeros of Random Analytic Functions

Zeros of Random Analytic Functions The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of generality. We study zeros of random analytic functions in one complex variable. It is known that there is a one parameter family o...