RAM required?

Of course the server needs RAM for normal operations of the operating system, as well as for processes like anti-virus software to run. The operating system will also use RAM to cache filesystem metadata, as well as act as a read cache for files. File servers don't benefit from large amounts of RAM like database servers do. Usually you won't see significant benefit beyond several GB of RAM, depending on the workload.

As long as the system has sufficient memory to hold everything without paging, any memory above that amount can reasonably be considered excess, though "supernumerary" might be a better term.  Excess memory is used by the kernel for disk caching.

So if the system is not paging due to insufficient memory, there will be a performance increase due to that disk caching, but it will be small.

I have 2 file servers in my network. Old one has 2 core processor and 16GB RAM and new one with 2 processors and 48GB ram.
No significant difference with speed, so I think you don;t need extra memory for file server if server itself is working OK.

Thanks to everyone who commented.

I agree - file services is a very lightweight service, RAM wise.  If you setup a file server with dynamic RAM in Hyper-V you see just how little RAM is really needed.

Exchange and SQL on the other hand are memory intensive.  The more RAM, the better the performance.  You might not notice it working on the servers, but both systems cache as much data as they can... if you have 1000 users of Exchange, certain tasks the end user does can be helped significantly with more RAM... but "everyday" usage might go relatively unnoticed.