[#P11166] Algebraicity of a Thue-Morse infinite product
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Problem. For each integer \(n\ge 0\), let \(t(n)\in\{0,1\}\) be the parity of the number of 1s in the binary expansion of \(n\), and set \(u(n)=(-1)^{t(n)}\). The convergent product \[Q=\prod_{n=1}^{\infty}\left(\frac{2n}{2n+1}\right)^{u(n)}=1.6281601297189172488\ldots\] is called a Thue-Morse infinite product. Determine whether \(Q\) is algebraic over \(\mathbb{Q}\).
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“Algebraicity of a Thue-Morse infinite product.” TheoremDB. P11166. Problem statement; statement identity tdbc1:703e417a15462b95b027b298b4014af13561fde49ddcb218e963d50b5543f245; statement text SHA-256 97585760f465d91fd221073660f99ac505eab2f9b2926dbadc1492d420aee73b. https://theoremdb.org/statement/?ref=P11166
@misc{theoremdb-problem-97585760f465d91fd221073660f99ac505eab2f9b2926dbadc1492d420aee73b,
title = {{Algebraicity of a Thue-Morse infinite product}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:703e417a15462b95b027b298b4014af13561fde49ddcb218e963d50b5543f245; statement text SHA-256 97585760f465d91fd221073660f99ac505eab2f9b2926dbadc1492d420aee73b},
url = {https://theoremdb.org/statement/?ref=P11166}
}Plain text: Built Markdown snapshot
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