Bounding the order of the central zero of a zeta function over a function field
Volume 189 / 2019
Acta Arithmetica 189 (2019), 391-395
MSC: Primary 11M26; Secondary 11M38.
DOI: 10.4064/aa180226-30-8
Published online: 3 June 2019
Abstract
We formulate an explicit formula for the zeta function for a function field $K$ of genus $g$ over a finite field $\mathbb{F}_q$, analogous to the Weil explicit formula. Then we give an upper bound for the multiplicity of the possible zero of the zeta function at the central point $s=1/2$.
