The paper under review deals with some theorems concerning the holomorphic functions in the unit disk that are vanishing on some circle integrals. Earlier, similar results were known only for the whole complex plane. As a result the author has solved Farkas' problem (see: \textit{L. Zalcman}, [Arch. Rat. Mech. Analysis 47, 237-254 (1972; Zbl 0251.30047)]. Let \(\mathbb{C}\) be the complex plane where \[ D_ r=\bigl\{ z \in \mathbb{C}: | z | \leq r \bigr\},\;D_ 1=D, \] and \(\partial D\) is the boundary of \(D\). If \(f \in C(D)\) and the integral of \(f\) vanishes on every circle tangent to \(\partial D\). Then \(f\) is holomorphic in \(D\). The paper is easily readable, the proofs are clearly understood and given in a straightforward manner using only unpretentious techniques such as some properties of Bessel functions.