On the exponent of distribution of the ternary divisor function
Abstract
We show that the exponent of distribution of the ternary divisor function d3 in arithmetic progressions to prime moduli is at least 1/2+1/46, improving results of Heath-Brown and Friedlander--Iwaniec. Furthermore, when averaging over a fixed residue class, we prove that this exponent is increased to 1/2 +1/34.
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