C++ ::  Writing A Function Template With Template Arguments?

I have a function:

template<class Iterator, class T>
void a(Iterator, Iterator, const T&);

and I want to be able to simplify calls to 'a' with calls like

a(someIteratableContainer);

instead of having to call:

a(someIteratableContainer.begin(), someIteratableContainer.end(), valueOfTheContainersElementType);

I also want to be able to generalize the function to handle any of the standard iteratable contains: array, vector, deque, whatever.

I was under the impression I could write:

template<template<class T> class U> a(U<T>& container) {
a(container.begin(), container.end(), g(T()));
}

where 'g()' returns an object of the element type. However, the compiler is claiming, no matter how I write a call to the overload, the original template is selected and/or the overload is invalid, depending on the various ways I attempt to write said overload.