Zeta functions of orders on surfaces

TL;DR

This paper introduces effective computational methods for determining the zeta functions associated with maximal orders on algebraic surfaces, advancing the ability to analyze their arithmetic properties.

Contribution

It presents novel algorithms specifically designed for computing zeta functions of maximal orders on surfaces, filling a gap in computational algebraic geometry.

Findings

Developed efficient algorithms for zeta function computation

Demonstrated methods on specific classes of surfaces

Enhanced understanding of arithmetic invariants of orders

Abstract

In this manuscript, we give effective methods for computing the zeta function of maximal orders on surfaces.