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- Title
Multiplicative Functions Resembling the Möbius Function.
- Authors
Liu, Qing Yang
- Abstract
A multiplicative function f is said to be resembling the Möbius function if f is supported on the square-free integers, and f (p)= ±1 for each prime p. We prove O- and Ω-results for the summatory function ∑n≤xf(n) for a class of these f, and the point is that these O-results demonstrate cancellations better than the square-root saving. It is proved in particular that the summatory function is O(x1/3+ε) under the Riemann Hypothesis. On the other hand it is proved to be Ω(x1/4) unconditionally. It is interesting to compare these with the corresponding results for the Möbius function.
- Subjects
MOBIUS function; RIEMANN hypothesis; SQUARE root
- Publication
Acta Mathematica Sinica, 2023, Vol 39, Issue 12, p2316
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-023-2259-7