On the exponent of distribution of the ternary divisor function

By 'Etienne Fouvry, Emmanuel Kowalski, P. Michel. 2013

64 citations recorded by the source corpus.

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 Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue class, we prove that this exponent is increased to 1/2 + 1/34.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ec96406facd504781e9f844892b97bece351ba19

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In Algebra and Number Theory

1. P. Michel
2. Emmanuel Kowalski
3. W. Sawin
4. Akshay Venkatesh
5. V. Blomer
6. Gergely Harcos
7. Shou-wu Zhang
8. M. Young

In Geometry and Topology

1. P. Michel
2. Emmanuel Kowalski
3. W. Sawin
4. Akshay Venkatesh
5. V. Blomer
6. M. Young
7. Shou-wu Zhang
8. R. Munshi

Citations in the corpus

• Bilinear forms with Kloosterman sums and applications (2015, methodology): “la we stated. 5.2. Decomposition of E(λf⋆1,x;q,a). Given any A> 1 as in Theorem 1.7, we fix some B> 1 sufficiently large (to depend on A). Given x> 2, we set L:= logx, ∆ = 1 +L−B. Arguing as in [FKM15c], we perform a partition of unity on the mand nvariables and decompose E(λf⋆1,x;q,a) into O(”