# maximum-modulus principle

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##### 2: 3.8 Nonlinear Equations
Initial approximations to the zeros can often be found from asymptotic or other approximations to $f(z)$, or by application of the phase principle or Rouché’s theorem; see §1.10(iv). …
##### 3: Bibliography R
• W. Rudin (1976) Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.
• ##### 4: 27.10 Periodic Number-Theoretic Functions
27.10.2 $f(n)=\sum_{m=1}^{k}g(m)e^{2\pi\mathrm{i}mn/k},$
27.10.3 $g(m)=\dfrac{1}{k}\sum_{n=1}^{k}f(n)e^{-2\pi\mathrm{i}mn/k}.$
27.10.7 $s_{k}(n)=\sum_{m=1}^{k}a_{k}(m)e^{2\pi\mathrm{i}mn/k},$
##### 5: 10.74 Methods of Computation
To ensure that no zeros are overlooked, standard tools are the phase principle and Rouché’s theorem; see §1.10(iv). …
##### 8: Bibliography L
• H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl (1923) The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Methuen and Co., Ltd., London.
• ##### 9: 3.6 Linear Difference Equations
Similar principles apply to equation (3.6.1) when $a_{n}c_{n}\neq 0$, $\forall n$, and $d_{n}\neq 0$ for some, or all, values of $n$. …
##### 10: Bibliography B
• M. Born and E. Wolf (1999) Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7th edition, Cambridge University Press, Cambridge.