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Primes in arithmetic progressions to smooth moduli

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  • UserJulia Stadlmann (Oxford)
  • ClockTuesday 13 February 2024, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jef Laga.

The twin prime conjecture asserts that there are infinitely many primes p for which p+2 is also prime. This conjecture appears far out of reach of current mathematical techniques. However, in 2013 Zhang achieved a breakthrough, showing that there exists some positive integer h for which p and p+h are both prime infinitely often. Equidistribution estimates for primes in arithmetic progressions to smooth moduli were a key ingredient of his work. In this talk, I will sketch what role these estimates play in proofs of bounded gaps between primes. I will also show how a refinement of the q-van der Corput method can be used to improve on equidistribution estimates of the Polymath project for primes in APs to smooth moduli.

This talk is part of the Number Theory Seminar series.

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