BandParityTower: the band-parity tower and its limit modulo eight
For a prime p let a = v_2(p-1), m = (p-1)/2^a, H_a the subgroup of (Z/p)^x of order m and s(x) = (-1)^ . The development proves the tower of band-parity laws of Paper I of the author's series: the cyclotomic tower (every coordinate of the band-parity sum of the character of order 2^a is congruent modulo 4 to an explicit count), the band-parity tower f_a = sum over H_a of s(u) s(u^2) = m (mod 4) at every odd prime, the doubling count sum over 2H_a of s(u) s(2u) = 2 N_a - m, the imaginary law e_a = 2 N_a - m (mod 4) at every prime p = 1 (mod 4) with its level-3 form, the collapse e_a = +-f_a…
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