Hong Ziwei, Zheng Zhiyong
Published 2025-06-23Version 1
In this paper, we analyze $C(x, y)$, the second moment of Ramanujan sums. Assuming the Riemann Hypothesis, we derive an asymptotic formula for $C(x, y)$ with improved error term precision. The key feature of our approach is that it allows $x$ and $y$ to be arbitrarily close.
Asymptotics for numbers of line segments and lines in a square grid
Asymptotic formula for sum-free sets in abelian groups
An Elementary Proof of an Asymptotic Formula of Ramanujan
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