>
> What about Nathanson, Melvyn B. (1996). *Additive number theory. The 
> classical bases* (ISBN 0-387-94656-X): could we use this textbook as a 
> reference?


I think it's an excellent reference, very detailed and self contained for 
the most part. It has some occasional typos/errors (what doesn't?) and does 
not prove facts like Siegel-Walfisz theorem; Waring's problem does not 
require that result, so it shouldn't be a problem at the beginning.

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