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Inspired by the "rough classification" ideas from additive  
combinatorics, Soundararajan and I have recently introduced the notion  
of pretentiousness into analytic number theory. Besides giving a more  
accessible description of the ideas behind the proofs of several well- 
known difficult results of analytic number theory, it has allowed us  
to strengthen several results, like the Polya-Vinogradov inequality,  
the prime number theorem, etc. In this talk we will introduce these  
ideas and gave some flavour of these developments.
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