Can someone enlighten me with the question in the next page: http://www.physicsforums.com/showthread.php?p=3208664#post3208664
I am asked to find all the modular forms with weight $k$ which don't have zeros on the upper half plane.
Can someone enlighten me with the question in the next page: http://www.physicsforums.com/showthread.php?p=3208664#post3208664
I am asked to find all the modular forms with weight $k$ which don't have zeros on the upper half plane.
The discriminant cusp form $\Delta$ is such a modular form, and its weight is twelve. It has a simple zero at infinity and no other zeroes. Suppose f is any modular form without zeroes in H. If f has a zero of order k at infinity, then $f/\Delta^k$ is a modular form with no zeroes or poles so it is constant. In particular the weight of f is $12k$.