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I seek a reference for the fact that "coefficients of the Hirzebruch $L$-polynomial have odd denominators". The coefficients are $$\frac{2^{2k}(2^{2k-1}-1)B_k}{(2k)!}$$ where $B_k$ is the Bernoulli number, but I cannot locate the appropriate divisibility property of $B_k$. Of course, $2^{2k-1}-1$ is odd, so it can be ignored.

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up vote 1 down vote accepted

This follows from the clausen - Von staudt theorem. See http://www.bernoulli.orG ( structure of the denominator)

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Thank you. One needs also a little combinatorial argument on how many powers of two are in $(2k)!$, but I think I got it. – Igor Belegradek Jun 4 '12 at 23:24

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