The Maximum Modulus Principle and Its Applications

M. Ram Murty and Purusottam Rath
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M. Ram Murty: Queen’s University, Department of Mathematics and Statistics
Purusottam Rath: Chennai Mathematical Institute

Chapter Chapter 5 in Transcendental Numbers, 2014, pp 19-22 from Springer

Abstract: Abstract The maximum modulus principle constitutes an essential tool in transcendence theory. Let us begin with a proof of this fundamental result. We fix the convention that a function is analytic in a closed set C if it is analytic in an open set containing C. A region is an open connected set. We consider the following version of the maximum modulus principle. The statement is not the most general, but suffices for our applications.

Keywords: Maximum Modulus Principle; Transcendental Theory; Fundamental Result; Essential Tool; Minimum Modulus (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-0832-5_5

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