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On the representation of friable integers by linear forms
Let P + (n) denote the largest prime of the integer n. Using the nilpotent Hardy-Littlewood method developed by Green and Tao, we give an asymptotic formula for where (F 1 , . . . , F t ) is a system of affine-linear forms of Z[X 1 , . . . , X d ] no two of which are affinely related and K is a convex body. This improves upon Balog, Blomer, Dartyge and Tenenbaum's work  in the case of product of linear forms.doi:10.4064/aa8153-9-2017 fatcat:xmxlf2xer5envp5mn37lixnovq