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math.NT2026
Non-orthogonality of the cubic and quartic large sieves via Rankin-Selberg
Alexandre de Faveri, Alexander Dunn, Jeffrey Hoffstein
We show unconditionally that the cubic and quartic large sieves are not perfectly orthogonal. The main obstruction to perfect orthogonality comes from the bias exhibited by Gauss s…
math.NT2026
Non-vanishing for quartic Hecke -functions and ranks of elliptic curves
Cruz Castillo, Alexandre de Faveri, Alexander Dunn
We show that a positive proportion of Hecke -functions attached to the quartic residue symbols for squarefree do not vanish…