复底数和复指数的幂函数的值分布定理
Distribution Theorem s for Values ofPower Functions with Complex Bases and Exponents
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摘要:用实变函数的理论讨论了复底数和复指数的幂函数w=tα的无穷多值的分布定理.在指数α为无理数 时,无穷多值稠密地分布在圆周上.当指数α为纯虚数时,无穷多值是孤立点集并分布在射线上.当α为复数(非 实数)时,无穷多值分布在对数螺线上.Abstract:By theorem of real funcion, the distribution theorems for infinite numberofvalues ofpower functionswith complex bases and exponentswere discussed. If the exponentαis an irrationalnumber, the the values are densely distributed on a circle. Ifαis a pure imaginary number, the values form an isolated setand are distributed on a ray. Ifαis a complex number (non-realnumber), the values are distributed on a logarithmic spiral.
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Key words:
- complex base/
- complex exponent/
- value/
- distribution/
- power function
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