S.E friends,

Due to my genuine interest to Goldbach's conjecture, I decided to self-study the subject of additive number theory on this upcoming Fall. Before jumping to such fascinating field of mathematics, I decided to self-study "introductory" number theory as I never took a number-theory course in past. While browsing through websites and libraries, I found books like Ireland/Rosen, Apostol, Nathanson,Hardy/Wright, Sierpinski, and Niven/Zuckerman/Montogomery. I really like them but I am not sure what book would be best for my plan to study additive number theory. Ireland/Rosen looks like it emphasizes algebraic aspect and assumes familiarity with elementary number theory from readers, Hardy/Wright and Apostol looks like an introduction to analytic number theory (which I am doubting if it is better idea to just start with additive number theory), etc. Currently, I fear that choosing wrong book might kill my curiosity to the number theory.

What books do you recommend to prepare for analytic number theory?

  • $\begingroup$ If you want the basics, a quick google search led me to this link: saylor.org/site/wp-content/uploads/2013/05/… Everything up to chapter 4 seems pretty straightforward. $\endgroup$ – JasonM Jul 9 '16 at 22:34
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    $\begingroup$ There is no such thing as the best book, there is only the best book for you, and that is something no one can know until after the fact. Having said that, I'd say Apostol, Hardy/Wright, and Niven/Zuckerman/Montgomery, the ones I'm most familiar with from your list, are all excellent choices. $\endgroup$ – Gerry Myerson Jul 9 '16 at 22:40

Well, Elementary number theory by David Burton. Number theory by Titu Andreescu are good for starters. Then you can move on to more advance books.

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  • $\begingroup$ Which one of these two do you think is better for mathematical olympiads? $\endgroup$ – Aryan Raina Apr 23 at 3:09

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