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SUMMARY:Primes of the form p^2 + nq^2 - Mehtaab Sawhney (Columbia Universi
 ty)
DTSTART:20251111T160000Z
DTEND:20251111T170000Z
UID:TALK235039@talks.cam.ac.uk
CONTACT:Julia Wolf
DESCRIPTION:Suppose that n is 0 or 4 modulo 6. We show that there are infi
 nitely many primes of the form p^2^+nq^2^ with both p and q prime\, and ob
 tain an asymptotic for their number. In particular\, when n=4 we verify th
 e `Gaussian primes conjecture' of Friedlander and Iwaniec. \n\nThe proof m
 akes heavy use of two recent developments in the theory of Gowers norms in
  additive combinatorics: quantitative versions of so-called concatenation 
 theorems\, due to Kuca and to Kuca--Kravitz-Leng\, and the quasipolynomial
  inverse theorem of Leng\, Sah and the speaker.
LOCATION:MR2\, CMS
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