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Explore the intricacies of the Hardy-Littlewood 3-tuple prime conjecture and its connection to convolutions of Ramanujan sums in this 44-minute lecture by Shivani Goel from IIIT-Delhi. Delivered as part of the 2023-2024 Fields Number Theory Seminar at the Fields Institute on November 6, 2023, delve into advanced number theory concepts and their applications. Gain insights into this complex mathematical topic and its significance in the field of prime number theory.