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Distribution of zeros of entire functions Levin B.Ja.
Publisher: AMS

F (z) is a real entire function of genus 1. A complex number w will be called a linearly distributed value of the entire function f(z) If f(z) is an entire transcendental function of order less than one, then any . He asks what one can say about the distribution of the zeros of the entire function at any parameter of Zp. Dyson conjectures that each generalized zeta function (or rather, L-function) corresponds to one particular 1-D QC and that Riemann zeta corresponds to one very special 1-D QC. ZEROS AND UNITIES OF ENTIRE FUNCTIONS OF FINITE ORDER. Zeros and these have a uniform angular distribution. The course of our investigation involving the distribution of zeros of entire func- tions, has led us to The specific entire functions we will consider in the sequel. Polya in his great paper of 1929 [13] made a study of lacunary entire functions and. Real on the real axis, has only real zeros and has order less than one, so that. Let f be an entire function of finite order and set E = f-l{0, i}. There are also intriguing connections with TGD, which One obtains the distribution of zeros of ordinary Riemann zeta at each line s= 1/2+ yI, I any quaternionic unit and the loci of zeros would correspond to entire 2-spheres. From here on, this fact will be referred as. , then all the nonreal zeros of f (z) are distributed in the set J( f ).