A smooth complex generalization of the Hobby-Rice theorem Oleg LazarevElliott Lieb 46Hobby-Rice theorem The Hobby-Rice Theorem states that, given $n$ functions $f_j$, there exists a multiplier $h$ such that the integrals of $f_jh$ are all simultaneously zero. This multiplier takes values~$\pm1$ and is discontinuous. We show how to find a multiplier that is infinitely differentiable, takes values on the unit circle, and is such that the integrals of $f_jh$ are all zero. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.5062 10.1512/iumj.2013.62.5062 en Indiana Univ. Math. J. 62 (2013) 1133 - 1141 state-of-the-art mathematics http://iumj.org/access/