Combinatorial and arithmetic identities based on formal group laws
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.
AMS Mathematics Subject Classification (1980)Primary 14L05, 55N22 Secondary 10A40, 55T15
Unable to display preview. Download preview PDF.
- S. Araki, "Typical formal groups in complex cobordism and K-theory", Lecture Notes in Mathematics, Kinokinuya Book Store (1974).Google Scholar
- A. Baker, F. Clarke, N. Ray, L. Schwartz, "The stable homotopy of BU and the Kummer congruences", submitted to Ann. Math., (1986).Google Scholar
- M. Hazewinkel, "Formal Groups and applications", Academic Press (1978).Google Scholar
- N. Katz, "p-adic L-functions for CM fields", Invent. Math. 49 (1978).Google Scholar
- The Manchester School of Topology, "Modular representations, the iterated S1-transfer, and the chromatic filtration", work in progress.Google Scholar
- H.R. Miller, "Universal Bernoulli numbers and the S1-transfer", in "Current Trends in Algebraic Topology", CMS-AMS (1982) 437–49.Google Scholar
- J. Riordan, "Combinatorial Identities", Academic Press.Google Scholar