I have written Professor X (Australia) for a Ph.D. position with my CV (in June) and he asked for 3 reference names in return. I sent it. As I did not write him seeing any advertisement so I waited. Meanwhile, I got busy with my own project and published two of my articles in highly reputed journals in these last three months. I did not get any response from Professor X yet. Should I write him back asking if he's still interested in me? Is it ok if I send him the links to my recent articles?
I would actually turn it around a bit.
Dear Professor X
We corresponded most recently a few months ago. I am still very interested in working with you toward a PhD if it can be made to happen. I haven't been idle in the interim. Following are links to my two most recent published articles. Please let me know if there is anything that I can do now to make this a reality.
Thank you ...
Rather than ask if they are interested, just say that you are interested as well as active.
How can I contact a professor after few months?
I would recommend writing a short, concise, email. There are other questions on this site where you might find advice for writing such an email.
Meanwhile, I got busy with my own project... I did not get any response from Professor X yet.
It is possible that your professor has also been busy and has other things on his mind.
Should I write him back asking if he's still interested in me?
If you are still interested in working with him, then yes.
Is it ok if I send him the links to my recent articles?
There should be no harm in including the links, but it might be good to phrase it in a way that requires no obligation on the part of the professor. Something as a progress update ("since we last corresponded, I have published this and this...") might be okay, but I would avoid asking him to read anything in particular.