Analytic approximation

利用逼近理论研究如下函数类的性质：全纯函数、亚纯函数、调和函数、次调和函数、多次调和函数和多次调和函数。要研究的两个特殊性质是值分布和普适性。我们希望表明，在所考虑的所有类别中，不仅普遍功能的存在，甚至普遍存在。特别是，我们将研究Riemann Zeta函数的普适性和值分布，特别是零值的分布，希望有助于解决Riemann假设。我们的方法是通过近似论，而不是数论。我们对值分布的研究是在内万林纳理论的意义上。

Approximation theory will be employed to investigate properties of functions belonging to the following classes: holomorphic, meromorphic, harmonic, subharmonic, pluriharmonic and plurisubharmonic. Two particular properties to be investigated are value distribution and universality. We hope to show, not only the existence, but even the prevalence, of universal functions in all classes considered. In particular, we shall investigate the universality propeties and value distribution of the Riemann zeta function   and specifically the distribution of zero values, in the hope of contributing towards a solution to the Riemann hypothesis. Our approach is via approximation theory, not number theory.Our study of value distribution is in the sense of Nevanlinna theory.