Claims

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1948_01_01_erdos: Erdős proves in 1948 that the sum of 1/(t^n-1) over n>=1 is irrational for every integer t with |t|>1, which settles every integer t>=2 and no non-integer rational t.

1994_01_01_bundschuh_vaananen: Bundschuh and Väänänen's 1994 Theorem 2, at alpha=-1, makes F(a/b) irrational, with an irrationality measure, for coprime a>b>=1 with log b/log a<1/2-1/pi^2; this covers every integer base and, for example, 7/2.

2026_09_11_cook: Cook's manuscript of September 2026 claims that F(a/b) is irrational for coprime a>b>=1 with log b/log a<0.40568..., which includes every power of 31/4; it does not cover 3/2 and has had no review.

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