# L-functions in Analytic Number Theory: Julia Stadlmann

## Event Recap

A <a href="https://mathtube.org/lecture/video/primes-arithmetic-progressions-smooth-moduli">recording</a> of this event is available on <a href="https://mathtube.org">mathtube.org</a>.

## Topic

Primes in arithmetic progressions to smooth moduli

## Details

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.

## Additional Information

A livestream option is available.

**Scientific, Seminar**

**March 4, 2024**

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