Why the author choose $s$ real?

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My question is: Why the author of this book (http://wstein.org/books/bsd/bsd.pdf) page 8 on Sec 1.4 choose $s$ real in despite that the variable is complex in the entire chapter. I am very confused about this fact.

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The Birch-Swinnerton-Dyer conjecture is about the value of $L(s,E)$ at $s=1$, so real valued is even more general.