Chromatic congruences and Bernoulli numbers
Abstract
For every natural number $n$ and a fixed prime $p$, we prove a new congruence for the orbifold Euler characteristic of a group. The $p$-adic limit of these congruences as $n$ tends to infinity recovers the Brown-Quillen congruence. We apply these results to mapping class groups and using the Harer-Zagier formula we obtain a family of congruences for Bernoulli numbers. We show that these congruences in particular recover classical congruences for Bernoulli numbers due to Kummer, Voronoi, Carlitz, and Cohen.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.17705
- arXiv:
- arXiv:2406.17705
- Bibcode:
- 2024arXiv240617705P
- Keywords:
-
- Mathematics - Algebraic Topology;
- Mathematics - Group Theory;
- Mathematics - K-Theory and Homology;
- Mathematics - Number Theory;
- 55R40;
- 57K20;
- 11B68;
- 11M06
- E-Print:
- 22 pages