CMI-IMSc Number Theory Seminar
Date: Tuesday, 27 August 2024
Time: 3:30 to 4:30 PM
Venue: Seminar Hall, CMI
On the Hardy-Littlewood k-tuple prime conjecture and convolutions of Ramanujan sums
Shivani Goel
Chennai Mathematical Institute.
27-08-24

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Abstract

The Hardy-Littlewood k-tuple prime conjecture is one of the most significant unsolved problems in mathematics. In 1999, Gadiyar and Padma presented a heuristic derivation of the 2-tuples conjecture by employing the orthogonality principle of Ramanujan sums. In this talk, we derive a limit formula for higher convolutions of Ramanujan sums and then apply this in conjunction with the general theory of arithmetical functions of several variables to give a heuristic derivation of the Hardy-Littlewood conjecture.