Complex conjugation acts on the vector space corresponding to the middle entry in the Hodge vector. The signature of a hypergeometric motive is the difference between the number of $+1$ eigenvalues and the number of $-1$ eigenvalues for this operator.
When there is no middle entry (because the Hodge width is odd), the signature is $0$.
The archimedean root number can be recovered from the signature $s$ and the Hodge vector $(h_n)$.
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- Last edited by David Roe on 2024-04-23 14:05:29
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