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Number theory
Date added
Erdős problem 1049
Let t>1 be a rational number. Is
∑n=1∞tn−11=∑n=1∞tnτ(n)
irrational, where
τ(n)
counts the divisors of
n
?
A conjecture of Chowla.
$2,714 bounty·nobody has started·1 proof submitted, last month
week of 18 Sept 2025 · nothing publishedweek of 25 Sept 2025 · nothing publishedweek of 2 Oct 2025 · nothing publishedweek of 9 Oct 2025 · nothing publishedweek of 16 Oct 2025 · nothing publishedweek of 23 Oct 2025 · nothing published
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
18 Sept 2025nothing published against this one yet10 Sept 2026
erdosproblems.com/1049
[Er48] Erdős, P., On arithmetical properties of Lambert series. J. Indian Math. Soc. (N.S.) (1948), 63-66.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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