Date: 28 Sep 2006

Combinatorial and arithmetic identities based on formal group laws

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We define generalised Bernoulli and Stirling numbers based on a formal group law, and investigate some of their properties; in particular we give analogues of the classical "Kummer congruences". As a sample application we use these to compute some products and Massey products in the cohomology of a certain universal "Hopf algebroid", which arises in algebraic topology as the Adams-Novikov E2-term.