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Value-distribution of quartic Hecke L-functions
- Source :
- Moscow Journal of Combinatorics and Number Theory. 10:167-181
- Publication Year :
- 2021
- Publisher :
- Mathematical Sciences Publishers, 2021.
-
Abstract
- Set $K=\mathbb{Q}(i)$ and suppose that $c\in \mathbb{Z}[i]$ is a square-free algebraic integer with $c\equiv 1 \imod{\langle16\rangle}$. Let $L(s,\chi_{c})$ denote the Hecke $L$-function associated with the quartic residue character modulo $c$. For $\sigma>1/2$, we prove an asymptotic distribution function $F_{\sigma}$ for the values of the logarithm of \begin{equation*} L_c(s)= L(s,\chi_c)L(s,\overline{\chi}_{c}), \end{equation*} as $c$ varies. Moreover, the characteristic function of $F_{\sigma}$ is expressed explicitly as a product over the prime ideals of $\mathbb{Z}[i]$.<br />Comment: 11 pages
- Subjects :
- Pure mathematics
Algebra and Number Theory
Mathematics - Number Theory
Logarithm
Distribution (number theory)
Characteristic function (probability theory)
Function (mathematics)
Prime (order theory)
Product (mathematics)
Quartic function
FOS: Mathematics
Discrete Mathematics and Combinatorics
Number Theory (math.NT)
Algebraic integer
11M41, 11R42
Mathematics
Subjects
Details
- ISSN :
- 26407361 and 22205438
- Volume :
- 10
- Database :
- OpenAIRE
- Journal :
- Moscow Journal of Combinatorics and Number Theory
- Accession number :
- edsair.doi.dedup.....3d64e6e9855dc084641ac0aa6202b5c0