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arXiv · 1602.03583

Divisor problem in arithmetic progressions modulo a prime power

Kui Liu·Igor E. Shparlinski·Tianping Zhang
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Abstract

We obtain an asymptotic formula for the average value of the divisor function over the integers $n \le x$ in an arithmetic progression $n \equiv a \pmod q$, where $q=p^k$ for a prime $p\ge 3$ and a sufficiently large integer $k$. In particular, we break the classical barrier $q \le x^{2/3}$ for such formulas, and generalise a recent result of R.~Khan (2015), making it uniform in $k$.

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Kui Liu, Igor E. Shparlinski, Tianping Zhang. 2016-02-11. Divisor problem in arithmetic progressions modulo a prime power. https://arxiv.org/abs/1602.03583

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