Divisibility of generalized exponential and logarithmic coefficients

Davis, Donald M.

doi:10.1090/S0002-9939-1990-1013968-3

Divisibility of generalized exponential and logarithmic coefficients
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by Donald M. Davis

Proc. Amer. Math. Soc. 109 (1990), 553-558

DOI: https://doi.org/10.1090/S0002-9939-1990-1013968-3

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Abstract:

We prove that for isomorphic formal group laws, the maximal $p$-power in the denominators of certain collections of coefficients of powers of their exponential series are equal. These numbers are significant in algebraic topology.

References

M. F. Atiyah and J. A. Todd, On complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 56 (1960), 342–353. MR 132552, DOI 10.1017/s0305004100034642
J. F. Adams and G. Walker, On complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 61 (1965), 81–103. MR 171285
Andrew Baker, Combinatorial and arithmetic identities based on formal group laws, Algebraic topology, Barcelona, 1986, Lecture Notes in Math., vol. 1298, Springer, Berlin, 1987, pp. 17–34. MR 928821, DOI 10.1007/BFb0082998
Martin Bendersky, Some calculations in the unstable Adams-Novikov spectral sequence, Publ. Res. Inst. Math. Sci. 16 (1980), no. 3, 739–766. MR 602467, DOI 10.2977/prims/1195186928
Francis Clarke, The universal von Staudt theorems, Trans. Amer. Math. Soc. 315 (1989), no. 2, 591–603. MR 986687, DOI 10.1090/S0002-9947-1989-0986687-3
Louis Comtet, Advanced combinatorics, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR 0460128
M. C. Crabb and K. Knapp, James numbers, Math. Ann. 282 (1988), no. 3, 395–422. MR 967021, DOI 10.1007/BF01460042
M. C. Crabb and K. Knapp, The Hurewicz map on stunted complex projective spaces, Amer. J. Math. 110 (1988), no. 5, 783–809. MR 961495, DOI 10.2307/2374693
Donald M. Davis and Mark Mahowald, $v_1$-periodic homotopy of $\textrm {Sp}(2), \textrm {Sp}(3),$ and $S^{2n}$, Homotopy theory and related topics (Kinosaki, 1988) Lecture Notes in Math., vol. 1418, Springer, Berlin, 1990, pp. 219–237. MR 1048189, DOI 10.1007/BFb0083706
I. Dibag, An analogue of the von Staudt-Clausen theorem, J. Algebra 87 (1984), no. 2, 332–341. MR 739937, DOI 10.1016/0021-8693(84)90140-6

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Michiel Hazewinkel, Formal groups and applications, Pure and Applied Mathematics, vol. 78, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506881
Albert T. Lundell, Generalized $E$-invariants and the numbers of James, Quart. J. Math. Oxford Ser. (2) 25 (1974), 427–440. MR 375312, DOI 10.1093/qmath/25.1.427
Haynes Miller, Universal Bernoulli numbers and the $S^{1}$-transfer, Current trends in algebraic topology, Part 2 (London, Ont., 1981) CMS Conf. Proc., vol. 2, Amer. Math. Soc., Providence, RI, 1982, pp. 437–449. MR 686158