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arXiv · 2304.11696

Smooth numbers in arithmetic progressions to large moduli

Alexandru Pascadi
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Abstract

We show that smooth numbers are equidistributed in arithmetic progressions to moduli of size $x^{66/107-o(1)}$. This overcomes a longstanding barrier of $x^{3/5-o(1)}$ present in previous works of Bombieri-Friedlander-Iwaniec, Fouvry-Tenenbaum, Drappeau, and Maynard. We build on Drappeau's variation of the dispersion method and on exponential sum manipulations of Maynard, ultimately relying on optimized Deshouillers-Iwaniec type estimates for sums of Kloosterman sums.

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Alexandru Pascadi. 2023-04-23. Smooth numbers in arithmetic progressions to large moduli. https://doi.org/10.1112/s0010437x2500747x

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