Vol. 10, No. 3, 2021

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Value-distribution of quartic Hecke $L$-functions

Peng Gao and Liangyi Zhao

Vol. 10 (2021), No. 3, 167–181
Abstract

Set K = (i) and suppose that c [i] is a square-free algebraic integer with c 1(mod16). Let L(s,χc) denote the Hecke L-function associated with the quartic residue character modulo c. For σ > 1 2, we prove an asymptotic distribution function Fσ for the values of the logarithm of

Lc(s) = L(s,χc)L(s,χ̄c)

as c varies. Moreover, the characteristic function of Fσ is expressed explicitly as a product over the prime ideals of [i].

Keywords
value-distribution, logarithm of $L$-functions, quartic characters
Mathematical Subject Classification
Primary: 11M41, 11R42
Milestones
Received: 26 August 2020
Revised: 23 May 2021
Accepted: 7 June 2021
Published: 13 September 2021
Authors
Peng Gao
School of Mathematical Sciences
Beihang University
Beijing
China
Liangyi Zhao
School of Mathematics and Statistics
University of New South Wales
Sydney
Australia