Abstract
We introduce the study of triple convolution Ramanujan sums and apply it to give a~heuristic derivation of the Hardy-Littlewood conjecture on prime 3-tuples without using the circle method. We also estimate the triple convolution of the Jordan totient function using Ramanujan sums.
Citation
Sneha Chaubey. Shivani Goel. M. Ram Murty. "On the Hardy-Littlewood prime tuples conjecture and higher convolutions of Ramanujan sums." Funct. Approx. Comment. Math. 69 (2) 161 - 175, December 2023. https://doi.org/10.7169/facm/2048
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