What are the fertile areas of research in Analytic Number Theory?

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My professor once told me that Analytic Number Theory was "dead," which at the time was something of a disappointment, and which I struggled to agree with. Surely any subject may appear inferrtile in periods when researchers do not study the subject? I was just wondering, is this a generally accepted view? What reasons would be behind such opinion, and what are the fertile directions of research in this field?

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These and these are some sample and well known open problems in Analytic Number Theory. Also look at this to have a flavor of the most recent 'gossip' in Analytic Number Theory world.