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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Murty, M.R., Rath, P. (2014). The Maximum Modulus Principle and Its Applications. In: Transcendental Numbers. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0832-5_5
Download citation
DOI: https://doi.org/10.1007/978-1-4939-0832-5_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-0831-8
Online ISBN: 978-1-4939-0832-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)