Value-distribution of quartic Hecke L-functions

摘要

Set K D Q(i) and suppose that c∈Z[i] is a square-free algebraic integer with c ≡ 1 (mod ). Let L(s, χ_c) denote the Hecke L-function associated with the quartic residue character modulo c. For σ > 1/2, we prove an asymptotic distribution function F_σ for the values of the logarithm of as c varies. Moreover, the characteristic function of Fσ is expressed explicitly as a product over the prime ideals of Z[i].