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apparently, the Dirichlet hyperbola method is no longer up-to-date, and instead Voronoi's identity is used in order to establish good bounds on the Dirichlet divisor problem. The same applies to the ...

I'm interested in summing $\tau(m)$, the number of positive divisors of $m$, not over all integers in an interval but rather over only the integers with the most divisors. More specifically: Given a ...

There is a large literature on Hooley's $$ \Delta(n)=\max_u\sum_{d|n,\ e^u\le d< e^{u+1}}1 $$ giving its normal and average order. What is known of its maximal order? Clearly $\Delta(n)\le d(n)$ ...