On the Möbius function in all short intervals
We show that, for the Möbius function $\mu(n)$, we have $$ \sum_{x < n\leq x+x^{\theta}}\mu(n)=o(x^{\theta}) $$ for any $\theta>0.55$. This improves on a result of Ramachandra from 1976, which is valid for $\theta>7/12$. Ramachandra's result corresponded to Huxley's $7...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
European Mathematical Society
2022
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