I found an (already published) paper that cites a paper of mine, but without inserting even the arXiv link (the paper is still in press). In this way, I lose one citation.
Is it possible for me to write the journal asking them to fix the problem?
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I will start with this:
Moreover, the citations on papers on arxiv count as an effective citation?
The answer to this cannot be objective. Different people (senior researchers) will give different answers depending on their research philosophy. Similarly, different bibliographic indices do (e.g. Google scholar consider the citations but others do not).
There are no standard rules obliging authors how to mention their references but I think most of the publishers (big ones especially) are keen to link the references to their sources. For some of my publications, I got contacted by the publisher before publishing my paper to fix a reference input because they were not able to link it.
In summary, I think there is no harm to contacting the journal asking to link the reference to your paper but you cannot contact every bibliographic index to do the same thing (e.g. Google Scholar, researchgrate, etc). Note that each of these indices has its own algorithm of linking papers to their citations (e.g. Google Scholar consider them non-source items and you can add it manually but I am not sure about the others). On the other side, you cannot track every citation and I think it is much better to invest time in making new publications that are worth citing.
In the future, you can improve the accessibility of your papers by publishing codes, data, etc. and using public repositories.