Shivani Goel (IIIT-Delhi)


Tuesday October 24, 2023
4:00 pm - 5:00 pm


Jeffery Hall, Room 319

Number Theory Seminar

Tuesday, October 24th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Shivani Goel (IIIT-Delhi)

Title: On the Hardy Littlewood 3-tuple prime conjecture and convolutions of Ramanujan sums.

Abstract: The Hardy and Littlewood k-tuple prime conjecture is one of the most enduring 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. Building upon their work, we explore triple convolution Ramanujan sums and use this approach to provide a heuristic derivation of the Hardy-Littlewood conjecture concerning prime 3-tuples. Furthermore, we estimate the triple convolution of the Jordan totient function using Ramanujan sums.