Terence Tao on Nostr: Vjeko Kovac and I just uploaded a preprint to the arXiv entitled "On several ...
Vjeko Kovac and I just uploaded a preprint to the arXiv entitled "On several irrationality problems for Ahmes series"
https://arxiv.org/abs/2406.17593 , making progress on several open problems of Erdos and of Stolarsky regarding when sums of reciprocals of natural numbers are rational or not. Perhaps the most striking result is that we can find an increasing sequence 𝑎ₙ of natural numbers with the property that ∑ₙ1/(𝑎ₙ+𝑡) converges to a rational for all rational 𝑡 for which the denominators are non-zero, answering a question of Stolarsky in the negative. More discussion at
https://terrytao.wordpress.com/2024/11/27/on-several-irrationality-problems-for-ahmes-series/Published at
2024-11-28 06:25:04Event JSON
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"content": "Vjeko Kovac and I just uploaded a preprint to the arXiv entitled \"On several irrationality problems for Ahmes series\" https://arxiv.org/abs/2406.17593 , making progress on several open problems of Erdos and of Stolarsky regarding when sums of reciprocals of natural numbers are rational or not. Perhaps the most striking result is that we can find an increasing sequence 𝑎ₙ of natural numbers with the property that ∑ₙ1/(𝑎ₙ+𝑡) converges to a rational for all rational 𝑡 for which the denominators are non-zero, answering a question of Stolarsky in the negative. More discussion at https://terrytao.wordpress.com/2024/11/27/on-several-irrationality-problems-for-ahmes-series/",
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