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NOTE ON FOURIER–STIELTJES COEFFICIENTS OF COIN-TOSSING MEASURES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 102 / Issue 3 / December 2020
- Published online by Cambridge University Press:
- 20 April 2020, pp. 479-489
- Print publication:
- December 2020
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- Article
- Export citation
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It is known that the Fourier–Stieltjes coefficients of a nonatomic coin-tossing measure may not vanish at infinity. However, we show that they could vanish at infinity along some integer subsequences, including the sequence
${\{b^{n}\}}_{n\geq 1}$ where 
$b$ is multiplicatively independent of 2 and the sequence given by the multiplicative semigroup generated by 3 and 5. The proof is based on elementary combinatorics and lower-bound estimates for linear forms in logarithms from transcendental number theory.
