Coefficients in powers of the log series

We determine the p-exponent in many of the coefficients in the power series (log(1+x)/x)^t, where t is any integer. In our proof, we introduce a variant of multinomial coefficients. We also characterize the power series x/log(1+x) by certain zero coefficients in its powers.Comment: 8 page

3-primary v1-periodic homotopy groups of E7

We compute the 3-primary v1-periodic homotopy groups of the exceptional Lie group E7. Now E8 at the primes 3 and 5 is the only compact simple Lie group whose odd-primary v1-periodic homotopy groups remian to be computed. The main work is computing the unstable Novikov spectral sequence of \Omega E7/Sp(2). Showing that this converges to v1-periodic homotopy groups requires recent work of Bousfield and Bendersky-Thompson.Comment: 51 pages. Submitted to New York Electronic Journal of Mathematic