diff --git a/CHANGELOG.md b/CHANGELOG.md
index aa01a33d4..b12f79c46 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,12 @@ and this project adheres to
 
 Changelogs for this project are recorded in this file since v0.2.0.
 
+## [v0.5.2]
+
+### Changed
+
+* In docs, change references to `master` branch to `main` branch.
+
 ## [v0.5.0]
 
 ### Changed
diff --git a/README.md b/README.md
index ae12e1294..ea4b0c810 100644
--- a/README.md
+++ b/README.md
@@ -45,7 +45,7 @@
 There are different alternatives to install tslearn:
 * PyPi: `python -m pip install tslearn`
 * Conda: `conda install -c conda-forge tslearn`
-* Git: `python -m pip install https://github.com/tslearn-team/tslearn/archive/master.zip`
+* Git: `python -m pip install https://github.com/tslearn-team/tslearn/archive/main.zip`
 
 In order for the installation to be successful, the required dependencies must be installed. For a more detailed guide on how to install tslearn, please see the [Documentation](https://tslearn.readthedocs.io/en/stable/?badge=stable#installation).
 
diff --git a/docs/installation.rst b/docs/installation.rst
index eeae41d7e..2dea6d422 100644
--- a/docs/installation.rst
+++ b/docs/installation.rst
@@ -31,7 +31,7 @@ repository hosted at github:
 
 .. code-block:: bash
 
-    python -m pip install https://github.com/tslearn-team/tslearn/archive/master.zip
+    python -m pip install https://github.com/tslearn-team/tslearn/archive/main.zip
 
 In this case, you should have ``numpy``, ``cython`` and C++ build tools
 available at build time.
diff --git a/tslearn/__init__.py b/tslearn/__init__.py
index fbe12bc11..6841a505d 100644
--- a/tslearn/__init__.py
+++ b/tslearn/__init__.py
@@ -1,7 +1,7 @@
 import os
 
 __author__ = 'Romain Tavenard romain.tavenard[at]univ-rennes2.fr'
-__version__ = "0.5.1.0"
+__version__ = "0.5.2"
 __bibtex__ = r"""@article{JMLR:v21:20-091,
   author  = {Romain Tavenard and Johann Faouzi and Gilles Vandewiele and
              Felix Divo and Guillaume Androz and Chester Holtz and
diff --git a/tslearn/metrics/dtw_variants.py b/tslearn/metrics/dtw_variants.py
index 4fb1ae3bb..83d45de60 100644
--- a/tslearn/metrics/dtw_variants.py
+++ b/tslearn/metrics/dtw_variants.py
@@ -1141,8 +1141,12 @@ def cdist_dtw(dataset1, dataset2=None, global_constraint=None,
 
     .. math::
 
-        DTW(X, Y) = \sqrt{\sum_{(i, j) \in \pi} (X_{i} - Y_{j})^2}
+        DTW(X, Y) = \sqrt{\sum_{(i, j) \in \pi} \|X_{i} - Y_{j}\|^2}
+    
+    Note that this formula is still valid for the multivariate case.
 
+    It is not required that time series share the same size, but they 
+    must be the same dimension.
     DTW was originally presented in [1]_ and is
     discussed in more details in our :ref:`dedicated user-guide page <dtw>`.