Primes of the form p^2 + nq^2

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• Mehtaab Sawhney (Columbia University)
• Tuesday 11 November 2025, 16:00-17:00
• MR2, CMS.

If you have a question about this talk, please contact Julia Wolf.

Note: This talk will unusually take place on a Tuesday.

Suppose that n is 0 or 4 modulo 6. We show that there are infinitely many primes of the form p²+nq² with both p and q prime, and obtain an asymptotic for their number. In particular, when n=4 we verify the `Gaussian primes conjecture’ of Friedlander and Iwaniec.

The proof makes 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.

This talk is part of the Discrete Analysis Seminar series.

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