On the exponent of distribution of the ternary divisor function

Étienne Fouvry; Emmanuel Kowalski; Philippe Michel

doi:10.1112/s0025579314000096

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arXiv · 1304.3199

On the exponent of distribution of the ternary divisor function

Étienne Fouvry·Emmanuel Kowalski·Philippe Michel

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Abstract

We show that the exponent of distribution of the ternary divisor function $d_3$ 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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Étienne Fouvry, Emmanuel Kowalski, Philippe Michel. 2014-01-27. On the exponent of distribution of the ternary divisor function. https://doi.org/10.1112/s0025579314000096

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