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Bilinear sums with $GL(2)$ coefficients and the exponent of distribution of $d_3$

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Prahlad Sharma
Alfréd Rényi Institute/MPIM
Wed, 27/09/2023 - 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar
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.


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