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Statement

Strict admissibility is defined on the Theorem 1 page.

Theorem 3 (p. 629). Let $\{\xi_n\}_{n=1}^\infty$ be a sequence of independent random variables, each uniformly distributed on $(0,1)$. Then:

1. there is a constant $c>0$ such that if $q>1$ and $\lambda>cq^3$, the sequence $\{(n+\lambda-1)^q/\xi_n\}$ is strictly admissible with probability greater than $1/2$;
2. there is a constant $\nu_0>1$ such that for every $\nu\in(1,\nu_0]$ the sequence $\{\nu^{(n-1)^{1/3}}/\xi_n\}$ is strictly admissible with probability greater than $1/2$.

Source. A. S. Belov and S. V. Konyagin, An estimate for the free term of a nonnegative trigonometric polynomial with integer coefficients (in Russian), Mat. Zametki 59 (1996), no. 4, 627--629. Theorem 3 on p. 629. The edition read is identified on the source card.

Read depth. Claims checked: the statement was read clause by clause on the printed page. The note prints no proofs.

Proof pointer

None in the note. The note says (p. 629) that either part gives the upper bound of Theorem 4.

Dependencies

None stated.

Bears on

• Problem 256: indirectly, through the upper bound of Theorem 4 and Corollary 2.