On the Zeta Functions of Supersingular Curves

TL;DR

This paper demonstrates that the L-polynomial of supersingular curves of genus g can be uniquely determined by fewer than g coefficients, simplifying their characterization.

Contribution

It introduces a novel result showing that supersingular curves have L-polynomials determined by fewer coefficients than previously known.

Findings

L-polynomial of supersingular curves is determined by fewer than g coefficients

Simplifies the understanding of supersingular curve invariants

Provides new insights into the structure of supersingular curves

Abstract

In general, the L-polynomial of a curve of genus $g$ is determined by $g$ coefficients. We show that the L-polynomial of a supersingular curve of genus $g$ is determined by fewer than $g$ coefficients.