Kavli Affiliate: Hsiao-Mei (Sherry) Cho
| First 5 Authors: [#item_custom_name[1, [#item_custom_name[2, [#item_custom_name[3, [#item_custom_name[4, [#item_custom_name[5| Summary:Let $ell$ be an odd prime, $q$ an odd prime power such that $q notequiv 0 pmod ell$, and $m$ the order of $q$ in $F_ell^times$. We propose an explicit $L$-polynomial of hyperelliptic function field $K:=F_q(T, sqrt[ell]T^2+aT+b)$ with $a, b in F_q$ and $a^2-4b ne 0$. Using our formula, we obtain the explicit closed formula for the class number of $K$, where $m$ is even or $m=fracell-12$.As an application, we compute the average class numbers for hyperelliptic function fields with genus up to $3$.| Search Query: arXiv Query: search_query=au:Cho OR all:Hsiao-Mei&id_list=&start=0&max_results=3Read More