How do I call static members of a template class?

1. There is no syntax for specifying that. There's little reason to make f a static method anyway. Make it a free function instead. If you must make it a static method for some reason, implement it in terms of a free function and merely call it.
2. Many compilers will probably do this for you automatically.

No -- if you don't want to use a template argument, don't declare the class with a template parameter. If you need the template argument for other members of the class, but don't need it in f, then move f out of the class.

The compiler doesn't know that A<T>::f() doesn't use type parameter T. So as it is, you must give the compiler a type any time you use f.

But when I'm designing a template class and I notice some members/methods don't depend on template parameters, I'll often move those up to a non-template base class.

class A_Base {
public:
  static void f();
};

template <class T> class A : public A_Base {
  // ...
};

Now A_Base::f(), A<int>::f(), and A<double>::f() really are all the same thing.