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Statement

$\Phi$ is the functional defined on the Theorem 2 page. The note calls this theorem its main result (p. 629).

Theorem 4 (p. 629). For all $x\ge3$,

$$\frac{\ln^2x}{\ln\ln x}\ll\Phi(x)\ll\ln^3x .$$

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 4 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. It says (p. 629) that either part of Theorem 3 gives the upper bound, and that the lower bound develops ideas of A. S. Belov, Mat. Zametki 30 (1981), no. 4, 501--515.

Dependencies

Theorem 3 for the upper bound.

Bears on

• Problem 256: indirectly. With Theorem 2 it gives Corollary 1, from which the note derives the bound on the problem's $f(n)$ in Corollary 2.