Value-distribution of quartic hecke l-functions

Peng Gao; Liangyi Zhao

doi:10.2140/moscow.2021.10.167

Value-distribution of quartic hecke l-functions

Peng Gao
, Liangyi Zhao

School of Mathematical Sciences

University of New South Wales

Research output: Contribution to journal › Article › peer-review

Abstract

Set K = (i) and suppose that c ∈ [i ] is a square-free algebraic integer with c ≡ 1 (mod 〈16〉). Let L(s, χ_c) denote the Hecke L-function associated with the quartic residue character modulo c. For σ >¹2^, we prove an asymptotic distribution function F_σ for the values of the logarithm of L_c (s) = L(s, χ_c) L(s, ¯χ_c) as c varies. Moreover, the characteristic function of F_σ is expressed explicitly as a product over the prime ideals of [i ].

Original language	English
Pages (from-to)	167-181
Number of pages	15
Journal	Moscow Journal of Combinatorics and Number Theory
Volume	10
Issue number	3
DOIs	https://doi.org/10.2140/moscow.2021.10.167
State	Published - 2021

Keywords

Logarithm of L-functions
Quartic characters
Value-distribution

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10.2140/moscow.2021.10.167

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title = "Value-distribution of quartic hecke l-functions",

abstract = "Set K = (i) and suppose that c ∈ [i ] is a square-free algebraic integer with c ≡ 1 (mod 〈16〉). Let L(s, χc) denote the Hecke L-function associated with the quartic residue character modulo c. For σ >12, we prove an asymptotic distribution function Fσ for the values of the logarithm of Lc (s) = L(s, χc) L(s, ¯χc) as c varies. Moreover, the characteristic function of Fσ is expressed explicitly as a product over the prime ideals of [i ].",

keywords = "Logarithm of L-functions, Quartic characters, Value-distribution",

author = "Peng Gao and Liangyi Zhao",

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TY - JOUR

T1 - Value-distribution of quartic hecke l-functions

AU - Gao, Peng

AU - Zhao, Liangyi

PY - 2021

Y1 - 2021

N2 - Set K = (i) and suppose that c ∈ [i ] is a square-free algebraic integer with c ≡ 1 (mod 〈16〉). Let L(s, χc) denote the Hecke L-function associated with the quartic residue character modulo c. For σ >12, we prove an asymptotic distribution function Fσ for the values of the logarithm of Lc (s) = L(s, χc) L(s, ¯χc) as c varies. Moreover, the characteristic function of Fσ is expressed explicitly as a product over the prime ideals of [i ].

AB - Set K = (i) and suppose that c ∈ [i ] is a square-free algebraic integer with c ≡ 1 (mod 〈16〉). Let L(s, χc) denote the Hecke L-function associated with the quartic residue character modulo c. For σ >12, we prove an asymptotic distribution function Fσ for the values of the logarithm of Lc (s) = L(s, χc) L(s, ¯χc) as c varies. Moreover, the characteristic function of Fσ is expressed explicitly as a product over the prime ideals of [i ].

KW - Logarithm of L-functions

KW - Quartic characters

KW - Value-distribution

UR - https://www.scopus.com/pages/publications/85120373942

U2 - 10.2140/moscow.2021.10.167

DO - 10.2140/moscow.2021.10.167

M3 - 文章

AN - SCOPUS:85120373942

SN - 2220-5438

VL - 10

SP - 167

EP - 181

JO - Moscow Journal of Combinatorics and Number Theory

JF - Moscow Journal of Combinatorics and Number Theory

IS - 3

ER -

Value-distribution of quartic hecke l-functions

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Keywords

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