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Prahlad Sharma: Bilinear sums with (GL(2)) coefficients and the exponent of distribution of (d_3)

Time: Fri 2024-02-23 10.00 - 10.50

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Prahlad Sharma (MPI Bonn)

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We obtain the exponent of distribution \(1/2+1/30\) for the ternary divisor function \(d_3\) to square-free and prime power moduli, improving the previous results of Fouvry–Kowalski–Michel, Heath-Brown, and Friedlander–Iwaniec. The key input is certain estimates on bilinear sums with \(GL(2)\) coefficients obtained using the delta symbol approach.