Patterson's first moment for cubic Gauss sums
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
Patterson's first-moment conjecture concerns the average of normalized cubic Gauss sums over primary Eisenstein primes. The formalization proves the sharp-cutoff asymptotic with main term $\frac65c_X^{5/6}/\log X$, where $c_=(2\pi)^{2/3}/(3\Gamma(2/3))$. It also proves the corresponding angular comparison for every integer Fourier mode and cancellation of order $o(X^{5/6}/\log X)$ for each fixed nonzero mode. All primary Eisenstein primes are included, without an extra conjectural premise.
Comparator links
| Result | Comparator statement |
|---|---|
| Patterson first moment and angular cancellation | PattersonFirstMoment.lean |