The problem of the distribution of the singular points of the sum of a series of exponential monomials on the boundary of the domain of convergence of the series is considered. Sufficient conditions are found for a singular point to exist on a prescribed arc on the boundary; these are stated in purely geometric terms. The singular point exists due to simple relations between the maximum density of the exponents of the series in an angle and the length of the arc on the boundary of the domain of convergence that corresponds to this angle. Necessary conditions for a singular point to exist on a prescribed arc on the boundary are also obtained. They are stated in terms of the minimum density of the exponents in an angle and the length of the arc. On this basis, for sequences with density, criteria are established for the existence of a singular point on a prescribed arc on the boundary of the domain of convergence. Bibliography: 27 titles.

中文翻译：

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一系列指数单项式之和在收敛域边界上的奇异点分布

考虑了一系列指数单项式之和的奇异点在该系列收敛域的边界上的分布问题。找到一个奇异点存在于边界上规定弧线上的充分条件；这些仅以几何术语表示。奇点的存在是由于在一个角度上的系列指数的最大密度与对应于该角度的会聚域边界上的弧长之间的简单关系。还获得了奇异点在边界上的指定弧线上存在的必要条件。它们以一个角度中的最小指数密度和弧长表示。在此基础上，对于具有密度的序列，确定在收敛域边界上的规定弧上是否存在奇异点的标准。参考书目：27种。