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Meromorphic Functions Sharing the Same Zeros and Poles

Meromorphic Functions Sharing the Same Zeros and Poles

Hinkkanen’s problem (1984) is completely solved, i.e., it is shown that any meromorphic function f of
one complex variable is determined by its zeros and poles and the zeros of f(j), for j = 1, 2, 3, 4.

Theorem 1.1 (Nevanlinna’s Five-value Theorem (Nevanlinna 1929)) If two meromorphic functions share
five values IM, then they are equal.
The number five of IM shared values cannot be reduced.
Example 1 Let f(z) = exp(z) and g(z) = exp(−z). Then f and g share four values 0, 1, -1, ∞ IM. But f and g are
Theorem 1.2 (Nevanlinna’s Four-value Theorem (Nevanlinna 1929)) If two meromorphic functions, f and
g, share four values CM, then f is a M¨obius transformation of g.

Tranquilpeak — A gorgeous responsive theme for Hugo blog framework

Tranquilpeak — A gorgeous responsive theme for Hugo blog framework


Hugo version of Tranquilpeak is a based on original Hexo version This version is simply a port to Hugo static site generator.

Please all the credit should be attributed to original Hexo version and its author Louis Barranqueiro.

Hugo version keeps every .js and .css files untouched from original Hexo version in order to enjoy futur original Hexo version updates or features!


Quick start

Authors: Louis Barranqueiro (LouisBarranqueiro) and Thibaud Leprêtre (kakawait)
Version: 0.3.1-BETA (based on Hexo version 1.9.1)
Compatibility: Hugo v0.20.1

General features:

Fully responsive
Optimized for tablets & mobiles
Configurable menu of the sidebar
Pages to filter tags, categories and archives
Background cover image
Beautiful about page
Support Open Graph protocol
Easily customizable (fonts, colors, layout elements, code coloration, etc..)
Support internationalization (i18)
Posts features:

Thumbnail image
Cover image
Responsive videos & images
Sharing options
Navigation menu
GitHub theme for code highlighting (customizable)
Image gallery
Tags for images (FancyBox), wide images, tabbed code blocks, highlighted text, alerts
Table of contents
Integrated services:

Google analytics
Facebook Insights

Academic — Create a beautifully simple personal or academic website

Academic — Create a beautifully simple personal or academic website

Academic is a framework to help you create a beautiful website quickly. Perfect for personal, student, or academic websites. Check out the latest demo of what you’ll get in less than 10 minutes.

Key features:

Easily manage your homepage, blog posts, publications, talks, and projects
Configurable widgets available for Biography, Publications, Projects, News/Blog, Talks, and Contact
Need a different section? Just use the Custom widget!
Write in Markdown for easy formatting and code highlighting, with LaTeX for mathematical expressions
Social/academic network linking, Google Analytics, and Disqus comments
Responsive and mobile friendly
Simple and refreshing one page design
Easy to customize