Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can anybody help me with this question:

If $f(z)$ is an entire periodic function and it has to periods $2$ and $2i$, how can I find all other periods?

share|cite|improve this question

1 Answer 1

If the function is entire, and has periods $2$ and $2i$, then it is bounded, and by Liouville, it is then a constant, so that any non-zero complex number is a period.

The above is well-known result in the early stages of the theory of elliptic functions. See, for example, Apostol's book "Modular Functions and Dirichlet Series in Number Theory" on page 5.

share|cite|improve this answer
Umm ... not Halmos ... –  GEdgar Dec 17 '12 at 14:46
Absolutely right - it is Apostol, sorry. –  Old John Dec 17 '12 at 15:18

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.