I have a simple question. I am reading an english math book about zeta function. The author speaks about the "moduli of zeros" and I don´t find any definition of it and I have no idea what it means, cause I am not a native english speaker. What does that phrase mean?
I would be pleased by quick help.
The image you provided clears things up. You are reading about Jensen's Theorem, which tells us information about where the zeros of holomorpic functions are located. Importantly, during the proof the author is relying on there not being any zeros on the disk of radius $r$, where $r \in [0, R]$ is allowed to vary; however, holomorphic functions can obviously have zeros, so how do we account for this?
The first thing to recall is that there must be finitely many zeros in the disk of radius $R$ by the Identity Theorem (unless we have the identically zero function).
Now, to answer the question at hand, what is meant by the moduli of zeros? The word "moduli" is the plural of "modulus", which in math means the same as "magnitude" or "size" relative to something; here, it is referring to the points at a fixed distance, which are precisely the points with the same absolute value (and thus "size"). These are the circles the author is considering; the finitely many values of $r$ in $[0, R]$ for which the circle of radius $r$ passes through a zero of the given holomorphic function. The author then shows these exceptional values do not affect the result by using local estimates (I would prefer Blashke factors as I feel they capture more of what is going on, but this is personal choice).
Edit: if you do not know much English, what I wrote might be confusing. Let me know if you have any questions. As a short summary, the moduli of zeros are the $r \in [0,R]$ where there exists $z$ with $|z| = r$ and $F(z) = 0$