mathlib4
mathlib4 copied to clipboard
feat(Analysis/Complex): periodic holo funcs factor through exponential
We show that a holomorphic function which is periodic with a real period h
is given by f z = F (exp (2 * pi * I * z / h))
for some holomorphic F
, and moreover, if f
is bounded as Im z -> infty
then F
extends holomorphically to q = 0
.
These results will be used in a subsequent PR to define q-expansions for modular forms.