Verification of the Weak Sarnak-Xue Density Hypothesis

This project contains a computer verification of the Weak Sarnak-Xue Density Hypothesis for $SO_{2n+1}(\mathbb R)$, as posed in the work of author Aviv Hendler as part of his Master's Thesis in Mathematics at the Hebrew University of Jerusalem, under the supervision of Dr. Shai Evra.

How to run this code:

There are two possible entry points to this project - verify_conjectures.py and print_tables.py (see below). Both entry points accept two integers parameters representing a range (inclusive) of values for the rank (n) of the groups SO_{2n+1}. For example:

python verify_conjectures.py 2 50

will verify that all conjectures from the paper hold for all the partitions in all of the groups SO_{2n+1}, where 2 <= n <= 50.

Outcome of each entry point:

1. By running verify_conjectures.py, the code will verify that all of the conjectures made in the paper. For each n in the given range, it will check that each of the conjectures hold, and will output the results to stdout.
2. By running print_tables.py, the code will generate a .tex file containing formatted tables with the calculated data of all partitions, for each n in the given range.