{"id":"palomar/PALOMAR-2026-10-20-000010","url":"https://github.com/jkfarland-bot/FixedOrderFactor-lean/tree/0149a0e54cb853c0ba07e8f59234751d7b8efb55","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-20-000010-v2.json","repo":"https://github.com/jkfarland-bot/FixedOrderFactor-lean","tags":["math.NT","msc:11M06","msc:11M20","msc:11R42","msc:68V20","analytic-number-theory","l-functions","random-models","dirichlet-characters"],"score":0,"title":"FixedOrderFactor: the order-r correction factor for mean squares of L(1, chi), and the factor 35/34","trust":"high","domain":"math.NT","source":"palomar","authors":["Joseph S. Farland"],"reviews":0,"subject":"math.NT","summary":"For an integer r >= 2 and a finite set N of primes, the random Euler product model for Dirichlet characters of order r replaces chi(q) by independent uniform r-th roots of unity. The development proves that the order-r local factor E|1 - z/q|^(-2) equals (1 + q^-r)/((1 - q^-2)(1 - q^-r)), that its ratio to the full-circle factor (1 - q^-2)^(-1), multiplied over the primes outside N, is zeta^(N)(r)^2 / zeta^(N)(2r), that this correction factor is also the sum of (ab)^-r over the coprime pairs of integers prime to N, and that the model mean is zeta^(N)(2) zeta^(N)(r)^2 / zeta^(N)(2r). The…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-21","reactions":{},"formalized":true,"formalizes":[{"title":"The factor 35/34: fourth powers in the mean square of L(1, chi) over quartic characters","identifier":"https://doi.org/10.5281/zenodo.23491467","relationship":"formalizes"}]}