 Factorized fourth moment for a bilinear quadratic exponential sum

ID: factorized-fourth-moment-for-a-bilinear-quadratic-exponential-sum

Factoring

r_{1}^{2} - r_{2}^{2} = (r_{1} - r_{2}) (r_{1} + r_{2})

and similarly in

t

separates diagonal contributions from a geometric sum. Grouping the three fixed factors by their product

m

bounds the off-diagonal fourth moment by

\sum_{m ≪ R T^{2}} τ_{4} (m) min (R, ∥ α m ∥^{- 1}) .

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