Ordinary two-point correlations and the corrected Elliott conjecture
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalization proves ordinary two-point cancellation for multiplicative functions. For the Liouville function on every fixed pair of nonproportional affine forms, the correlation sum up to $X$ is $O(X/(\log X)^c)$ for an absolute $c>0$, with the implied constant depending on the forms.
For two one-bounded multiplicative functions, if at least one is uniformly nonpretentious against all Dirichlet-character twists with frequency $|t|\le N$, then their shifted and nonproportional affine correlation sums divided by $N$ tend to zero. These are ordinary averages, with no logarithmic averaging.
Comparator links
| Result | Comparator statement |
|---|---|
| Ordinary Elliott cancellation under uniform nonpretentiousness | OrdinaryElliott.lean |
| Ordinary Liouville and multiplicative two-point correlations | OrdinaryTwoPointCorrelations.lean |