On the sum of $Δ_{k}(n)$ in the Piltz divisor problem for $k=3$ and $k=4$
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Abstract
Let $Δ_{k}(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n\leq x}d_{k}(n)$, where $d_{k}(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet series $\sum_{n=1}^{\infty}Δ_{k}(n)n^{-s}$ and use Perron's formula to estimate the sums $\sum_{n\leq x}Δ_{3}(n)$ and $\sum_{n\leq x}Δ_{4}(n)$ for large $x>0$.
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All Related Versions
- Version 1, 2024-12-15, ArXiv
- Published version: Acta Arithmetica, 216 (4), 291.
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