Update README

.vscode/ltex.dictionary.en-US.txt

@@ -3,3 +3,5 @@ holomorphic
 integrability
 codiscrete
 meromorphy
+prover
+mathlib

.vscode/ltex.hiddenFalsePositives.en-US.txt

@@ -0,0 +1 @@
+{"rule":"MORFOLOGIK_RULE_EN_US","sentence":"^\\QHarmonic functions in the complex plane\nLaplace operator and associated API\nDefinition and elementary properties of harmonic functions\nMean value properties of harmonic functions\nReal and imaginary parts of holomorphic functions as examples of harmonic functions\nHolomorphic functions in the complex plane\nExistence of primitives [duplication of work already under review at mathlib]\nExistence of holomorphic functions with given real part\nMeromorphic Functions in the complex plane\nAPI for continuous extension of meromorphic functions, normal form of meromorphic functions up to changes along a discrete set\nBehavior of pole/zero orders under standard operations\nZero/pole divisors attached to meromorphic functions and associated API\nExtraction of zeros and poles\nIntegrals and integrability of special functions\nInterval integrals and integrability of the logarithm and its combinations with trigonometric functions; circle integrability of log ‖z-a‖\nCircle integrability of log ‖meromorphic‖\nBasic functions of Value Distribution Theory\nThe positive part of the logarithm, API, standard inequalities and estimates\nLogarithmic counting functions of divisors\nNevanlinna heights of entire meromorphic functions\nProximity functions for entire meromorphic functions\nJensen's formula\nNevanlinna's First Main Theorem\\E$"}

README.md

@@ -2,25 +2,32 @@
 
 ### Formalizing Value Distribution Theory
 
-This project aims to formalize value distribution theory for meromorphic
+This project aims to formalize [value distribution
-functions in the complex plane, roughly following the sections on Nevanlinna
+theory](https://en.wikipedia.org/wiki/Value_distribution_theory_of_holomorphic_functions)
-Theory in Serge Lang's "Introduction to Complex Hyperbolic Spaces". The project
+for meromorphic functions in the complex plane, roughly following Serge Lang's
-uses the lean4 computer language and builds on the lean mathematical library.
+[Introduction to Complex Hyperbolic
+Spaces](https://link.springer.com/book/10.1007/978-1-4757-1945-1). The project
+uses the [Lean](https://lean-lang.org/) theorem prover and builds on
+[mathlib](https://leanprover-community.github.io/), the Lean mathematical
+library.
 
-We are looking for collaborators. Please be in touch if you would like to join
+### Help Wanted
+
+Please be in touch if you would like to join
 the fun!
 
-## State of Affairs and Future Plans
+## Current State and Future Plans
 
-With the formalization of "Nevanlinna's First Main Theorem", the project has
+With the formalization of Nevanlinna's [First Main
-recently reached its first milestone. The current code has "proof of concept"
+Theorem](https://en.wikipedia.org/wiki/Nevanlinna_theory#First_fundamental_theorem),
-quality: It compiles fine but needs refactoring and documentation. The next
+the project has recently reached its first milestone. The current code has
-goals are as follows.
+"proof of concept" quality: It compiles fine but needs refactoring and
+documentation. Next goals:
 
-- Clean up the existing codebase and feed intermediate results into the lean
+- Clean up the existing codebase and feed intermediate results into mathlib
-  mathematical library
 - Formalize the Theorem on Logarithmic Differentials
-- Formalize the Second Main Theorem of value distribution theory
+- Formalize the [Second Main
+  Theorem](https://en.wikipedia.org/wiki/Nevanlinna_theory#Second_fundamental_theorem)
 - Establish some of the more immediate applications
 
 These plans might change, depending on feedback from the community and specific
@@ -28,7 +35,7 @@ interests of project participants.
 
 ## Material Covered
 
-We touched on the following subjects.
+The following concepts have been formalized so far.
 
 - Harmonic functions in the complex plane
     - Laplace operator and associated API
@@ -37,7 +44,8 @@ We touched on the following subjects.
     - Real and imaginary parts of holomorphic functions as examples of harmonic
       functions
 - Holomorphic functions in the complex plane
-    - Existence of primitives [duplication of work already under review at
+    - Existence of primitives [duplication of work [already under
+      review](https://github.com/leanprover-community/mathlib4/pull/9598) at
       mathlib]
     - Existence of holomorphic functions with given real part
 - Meromorphic Functions in the complex plane
@@ -56,5 +64,6 @@ We touched on the following subjects.
     - Logarithmic counting functions of divisors
     - Nevanlinna heights of entire meromorphic functions
     - Proximity functions for entire meromorphic functions
-- Jensen's formula
+- [Jensen's formula](https://en.wikipedia.org/wiki/Jensen%27s_formula)
-- The First Main Theorem
+- Nevanlinna's [First Main
+  Theorem](https://en.wikipedia.org/wiki/Nevanlinna_theory#First_fundamental_theorem)