I am looking a proof of Parseval's identity for Dirichlet series, if it is possible a free source or well if you know and it is possible get an idea of the proof a such theorem.
I am saying the quantitative version of Parseval's theorem for Dirichlet series, I mean the Lema 2.3.5 in page 48 of this (in spanish but is a concise formula, in the last paragraph) Granados, La distribución de los ceros de la función zeta de Riemann, (2014), available from this web of the Universidad Autónoma de Madrid.
Question. I am interested in details of a proof of the quantitative version of Parseval's identity for Dirichlet series. Do you know some reference where can I read it (if there is a free access it is the best)? Alternatively, if it is possible, provide us an outline or some idea to get such proof. Thanks in advance.
I recommend the above reference because has very high quality. I believe that there are no reference of such Lema 2.3.5 in the above text.