Mathematics colloquium

Wednesday, 17 January, 2023, 4 pm

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Venue: Ramanujan Hall

Host: Ravi Raghunathan

Speaker: R. Balasubramanian

Affiliation: Institute of Mathematical Sciences, Chennai

Title:  Product of three primes in an arithmetic progression

Abstract. Linnik proved that there exists a positive constant c such that the set {p: p is a prime ≤ q c} contains all invertible residue classes mod q. The original value of c was very large. The best known is c = 5 . It is expected to be true for any c > 2. We ask an analogous question What is the value of c for which we can claim that the set {p_1p_2p_3: p_i ≤ q c for i = 1, 2, 3} covers all invertible residue classes mod q . We shall explain how additive combinatorics naturally enters into the proof. This is a joint work with Ramare and Priyamvad Srivastav.