Let 0<α<1 be an irrational number and s be a real number. If the irrational number number α has bounded partial quotients, the function $exp(2\pi is \chi_{[o,t)}$ on the unit circle is a constant multiple of coboundary if and only if t is an integer multiple of α. However, if the irrational α has unbounded partial quotients, it is unknown for which t $exp(2\pi is \chi_{[o,t)}$ is a constant multiple of coboundary.
Let both $r_1$ and $r_2$ are rational numbers and α be any irrational number. In this paper, it is shown that for any real s, the function $exp(2\pi is \chi_{[0,r_1\alpha+r_2)}$ is a constant multiple of a cobaundary if and only if $r_1,r_2$ are integer.
α가 무리수이고 $r_1 r_2$가 유리수일 때 실수 s 에 대하여, 함수 $exp(2\pi is\chi_{[0,r_1+r_2)}$가 coboundary의 상수배일 필요 충분 조건은 $r_1$ 과 $r_2$가 정수임을 보였다.
