Why urxvtc doesn't accetp zsh functions when called with a "-c" argument?

In order to launch a new terminal and run a zsh function on it, I am trying to run the following command from within an urxvtc terminal (the urxvtd is running as a systemd service)

     urxvtc -e zsh -c "my-zsh-defined-function"

which doesn't work as the function is unknown. I need to explicitly source my zshrc to make it work

     urxvtc -e zsh -c "source ~/.zshrc; my-zsh-defined-function"

The problem is, I don't understand why. Shouldn't zsh source .zshrc as when I run urxvtc, and then I type my-zsh-defined-function ?