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Divisor function

Let $K$ be a number field. For a non-zero ideal $\mathfrak a$, write $t(\mathfrak a)$ for the number of its divisors (in the multiplicative monoid of non-zero ideals). It's called the divisor function. I wanted to type tau but as always ha…

Vaughan's decomposition 2

In the previous post we estimated the first term on the right hand side of: \[ \mathbb E_{N^{0.9} < n \le N }\mu (n)\bar f(n) = - \mathbb E_{N^{0.9}<n\le N } \sum _{b\le U,c\le V , bc|n } \mu (b) \mu (c) \bar f(n) + \mathbb E_{N^{0.9}<n\le N } \sum _{b> U,c> V , bc|n } \mu (b) \mu (c) \bar f(n) . \]…</n\le>