A new look at the McIntyre conjecture

As it is known the sum of any Dirichlet series is not bounded on the positive ray if and only if its exponents satisfy the Fejer condition (the Macintyre-Evgrafov theorem). In 1952 MacIntyre conjectured that an entire function with Fejer gaps is unbounded on any curve going to infinity.
We present a new result which allows us to refine the formulation of the problem in the report.