Over all primary Eisenstein primes of norm at most X, the sum of normalized cubic Gauss sums has the sharp-cutoff asymptotic (6/5)c₍*₎X^(5/6)/log X, where c₍*₎=(2π)^(2/3)/(3Γ(2/3)).
Over all primary Eisenstein primes of norm at most X, the sum of normalized cubic Gauss sums has the sharp-cutoff asymptotic (6/5)c₍*₎X^(5/6)/log X, where c₍*₎=(2π)^(2/3)/(3Γ(2/3)).
Over all primary Eisenstein primes of norm at most X, the sum of normalized cubic Gauss sums has the sharp-cutoff asymptotic (6/5)c₍*₎X^(5/6)/log X, where c₍*₎=(2π)^(2/3)/(3Γ(2/3)).
If correct, settles Patterson’s first-moment conjecture without the earlier GRH premise.
Does Patterson’s predicted first moment hold unconditionally?
Publication dates and editorial changes.
OpenAI reports an unconditional first moment for cubic Gauss sums
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