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Chromatic congruences and Bernoulli numbers
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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.
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Cited by 1 Pith paper
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Higher-Order Congruence for Reciprocal Power Sums and Generalized Lehmer-Type Products
Odd-order reciprocal power sums satisfy a uniform Bernoulli-polynomial congruence modulo n, and Lehmer-type products admit truncated Bell-polynomial expansions modulo n^{K+1}.
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