The least almost-prime in an arithmetic progression

Time: 9:30 -- 11: 00, March 18, 2026

Venue: Room 612, A6, Institute of Mathematics-VAST

Abstract: Given an integer sequence, a basic quest in number theory is to count numbers in this sequence with interesting multiplicative properties, such as primes and almost-primes. Towards this goal, sieve methods are designed to combinatorially extract simple divisibility properties of a sequence and combine with analytic tools for estimating sums and integrals to yield the desired arithmetic information.  In this talk, I will introduce fundamental sieve methods to count primes and almost-primes. I will describe our recent progress in estimating the least almost-prime in an arithmetic progression. This is joint work with Hà Minh Dũng and Hoàng Đức Anh.