Can I override the static functions?

Static functions are class-specific. You can declare/define functions with the same signature for other classes, but static functions either have to be accessed with classname::functionname() if accessed outside of the class, or simply functionname() if inside the class. They are NOT inherited by sub-classes. So, overriding them doesn't work like it would for member functions.

To be clear, no, you cannot override static methods. (You can overload them, though.)

The reason is simple: a static method cannot appear in a class's virtual function table, so it is not inherited. In order to call a static method you must know exactly what type of object you are calling it from.

A quick example:

#include <iostream>

struct Foo
{
  static void speak()
  {
    std::cout << "Hello\n";
  }
};

struct Bar: public Foo
{
  static void speak()
  {
    std::cout << "No.\n";
  }
};

int main()
{
  Foo* baz = new Bar;
  baz->speak();
}

Give it a run.

Even though it is actually a Bar you've got, the compiler sees that you've got a pointer to a Foo and calls Foo::speak().

What would you have to do to make it say "No"?

That's right. Cast.

static_cast <Bar*> (baz)->speak();

By now, you may wonder if using the pointer stuff isn't overkill.

Well, actually, it is. You might as well just call the static methods directly.

Foo::speak();
Bar::speak();

Hope this helps.