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arXiv · 1809.09822

Value-distribution of quartic Hecke $L$-functions

Peng Gao·Liangyi Zhao
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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 $L(s,χ_{c})$ 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 \begin{equation*} L_c(s)= L(s,χ_c)L(s,\overlineχ_{c}), \end{equation*} as $c$ varies. Moreover, the characteristic function of $F_σ$ is expressed explicitly as a product over the prime ideals of $\mathbb{Z}[i]$.

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Peng Gao, Liangyi Zhao. 2021-05-24. Value-distribution of quartic Hecke $L$-functions. https://doi.org/10.2140/moscow.2021.10.167

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