MellinDuality: Mellin duality for the band-parity companion
For an odd prime p, an odd character chi modulo p and m >= 0, the multiplier family C(a) = sum over 0 ) has Fourier transform over the characters 2 sum_a conj(psi)(a) C(a) = G(conj psi) G(chi psi^(2m)), with the multiplier constant G(psi) = sum_m psi(m) (-1)^m = 2 (1 - 2 psi(2)) B_(1,psi). The development proves this Mellin duality over any commutative ring, its inversion over the odd complex characters and its form bilinear in first Bernoulli numbers, the half-sum identity, the exponent family and its two collapses. At p = 5 (mod 8), for the quartic character, it proves the coset…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-11-02-000019
curl -X POST /api/v1/records/palomar/PALOMAR-2026-11-02-000019/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-11-02-000019/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'