FixedOrderFactor: the order-r correction factor for mean squares of L(1, chi), and the factor 35/34
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…
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