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Question: What would be some must-read papers for an aspiring analytic number theorist? In other words, what are the papers that any analytic number theorist would have read? (Background: Someone who has seen some classical analytic number theory, at the level of Davenport and modular forms books by Iwaniec)

There are some classical papers that comes to mind. For example,

  • Duke-Friedlander-Iwaniec's work on subconvexity bounds
  • Iwaniec's 1987 paper on bounding Fourier coefficients of half-integral weight modular forms
  • Duke's work on Linnik's problems

Basically I would like to collect papers that any graduate student in analytic number theory should have read/should be aware of. In particular I am interested in something more modern (although very classical papers such as Riemann's memoir is still welcome, for the sake of completeness) Thank you.

Edit: In light of Professor Garrett's comment, I am trying to restrict the scope a little bit. (Hopefully it's now more reasonable) Analytic number theory is a pretty diverse area, but hopefully there is a reasonable list of papers that every analytic number theorist would have read/know about.

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There are probably at least 100, if not a large factor more... if only because "analytic number theory" has many different senses, and many different corresponding notions of "background". Surely a list of 1000 papers would not be a desired answer... Clarification is needed, or else some sort of acknowledgement of "oops, so there's no royal road..."? – paul garrett Feb 27 '13 at 23:14
I feel like Iwaniec and Kowalski's "Analytic Number Theory" is a great guide to the further literature. I would suggest to an aspiring analytic number theorist that he or she first read Davenport, then start reading parts of IK, then follow up on whichever parts of IK seem most interesting. "Opera de Cribro" by Friedlander and Iwaniec is another great book that discusses much of the very recent literature. Also, Soundararajan has some excellent survey papers (such as "The Distribution of the Primes") with more references. There's much more out there, I am interested in other responses too. – Frank Thorne Feb 28 '13 at 3:18
This needs to be CW, I guess. – Marc Palm Feb 28 '13 at 7:40
I'd venture to bet that now with your restriction, taken in a strict sense, you are asking for the empty-set. I doubt there is even a single paper everybody (or even almost everybody) that qualifies as analytic number theorist has read. On a more serious note: what books have you already read? – user9072 Feb 28 '13 at 10:24
This question is too broad and your background is unclear. I am not an analytic number theorist, but I'll throw in my two cents. Weil's "explicit formula" paper and the paper where he proves the converse to Hecke's lemma. Selberg's collected works. – Felipe Voloch Feb 28 '13 at 12:35

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