Current Developments in Mathematics

Three topics in additive prime number theory

Ben Green

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We discuss, in varying degrees of detail, three contemporary themes in prime number theory. Topic 1: the work of Goldston, Pintz and Yıldırım on short gaps between primes. Topic 2: the work of Mauduit and Rivat, establishing that 50% of the primes have odd digit sum in base 2. Topic 3: work of Tao and the author on linear equations in primes.

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Current Developments in Mathematics Volume 2007 (2009), 1-41.

First available in Project Euclid: 5 October 2009

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Green, Ben. Three topics in additive prime number theory. Current Developments in Mathematics 2007 (2009), 1--41.

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