#### IMSc Webinar

#### Product of three primes in Arithmetic progression

#### R. Balasubramanian

##### IMSc

*By a result of Linnik , we know the the least prime in an arithmetic progression a ( mod q ) is bounded by a power of q . The best exponent known is 5.18 using analytic methods. Let , for any integer j , P_j denote the set of integers having exactly j prime factors ( counted with multiplicity ) If we are interested in the least element of P_j ( for j atleast 3 ) in the progression a ( mod q ) , then we can use both the analytic methods and additive combinatorics. We shall introduce additive combinatorics and explain how one can use this estimating the least element in P _j which is in a ( mod q ).*

Google meet link: meet.google.com/vas-mjgc-zdt

Done