QuadraticFloorII: fibre sums and quartic traces at conductor 8lp
Source: github.com/jkfarland-bot/QuadraticFloorII/tree/86f0b48f6a93…
Sequel to QuadraticFloor. For an odd prime p, the alternating floor sums S_{A,B,C}(p) = sum over 0 <= n < p of (-1)^floor((A n^2 + B n + C)/p) with admissible (B, C) are averages of first Bernoulli numbers of the odd characters vartheta_{p,psi} = eta_p chi_{-4}^delta psi modulo 8Ap. The development proves that, weighted by psi_0(b)^2 and summed over the units b modulo A, these sums give minus the sum of B_{1,vartheta_{p,psi}} over the fibre psi^2 = psi_0^2, which is real when psi_0^4 = 1; that for a prime l = 1 (mod 4), a quartic character xi modulo l and an odd prime p != l the real part of…
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