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

8 Connections Between Growth and Distribution of Zeros. ZEROS AND UNITIES OF ENTIRE FUNCTIONS OF FINITE ORDER. A theoretical explanation of the observed phenomenon of multiple resonance is given using classical results of the distribution of zeros of entire functions. This can be analytically continued to a function meromorphic on the entire complex plane, holomorphic everywhere except for a simple pole at {s=1} . Since the set of zeros of the entire function is contained in the set of zeros of , we see that the function is an entire function on the parameter . Also, we the only zeros of {\zeta} are the so-called 'trivial zeroes' at {s=-2,-4,\hdots} . Of the most important problems in the theory of entire functions is the distribution of the zeros of entire functions. One of the most important problems in the theory of entire functions is the distribution of the zeros of entire functions. Some Questions on the Distribution of Zeros of Entire Functions of Several Variables. Let G(z) be a real entire function of order less than 2 with only real zeros. We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. Chapter 2 General Properties of Entire Functions of Finite Order. On the Distribution of zeros of Entire Exponential Type Almost-Periodic Functions . Gaspar Mora Martınez and Juan Matıas Sepulcre Martınez. Let and be nonconstant entire functions, and let be an integer. Let f be an entire function of finite order and set E = f-l{0, i}. From (38), is an entire function of order of . The functional equation also shows that zeros are symmetrically distributed about the line {\Re(s)=1/2} .